Seminari periodici
DIPARTIMENTO DI MATEMATICA

Seminari di Analisi Matematica Bruno Pini

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Giovedì
26 Maggio
Tobias Weth
The fractional Poisson problem and the logarithmic Laplacian

seminario di analisi matematica

 ore 16:00
  presso Aula Seminario VIII piano
seminario on line • collegamento al meeting su zoom
I will discuss some recent results on the family of fractional Poisson problems $(-\Delta)^s u =f$ in $\Omega$, $u=0$ on $\Omega^c$ of order $2s$ and its connection to the logarithmic Laplacian operator. This connection allows, in particular, to characterize the $s$-dependence of solutions to this family. Special attention will be given to the case $f\equiv 1$, i.e., the fractional torsion problem. This is joint work with Sven Jarohs and Alberto Saldana.

Giovedì
16 Giugno
Cristian Gutierrez (Temple University)
TBA

seminario di analisi matematica

 ore 16:00
  presso Aula Tonelli
seminario on line • collegamento al meeting su zoom

Seminari passati


2022
19 Maggio
Bruno Franchi
Teoria Geometrica della Misura nei gruppi di Carnot e sottovarietà intrinseche (Geometric Measure Theory in Carnot groups and intrinsic submanifolds).

seminario di analisi matematica

Carnot groups provide the simplest instance of metric spaces that are non-Riemannian but are still endowed with a rich structure of dilations and translations, making possible to develop a non-Riemannian Geometric Measure Theory. The first step of this program consists in the search of a good (i.e natural) notion of regular submanifolds and in the study of their properties. In this talk we present few chapters of this program along the guidelines of a joint monograph with Raul Serapioni and Francesco Serra Cassano, Some topics of Geometric Measure Theory in Carnot Groups (in preparation). - I gruppi di Carnot forniscono l'esempio più semplice di spazi metrici che non sono riemanniani ma che sono comunque dotati di una ricca struttura di dilatazioni e traslazioni che permettono di sviluppare una Teoria geometrica della misura non riemanniana. Il primo passo di questo programma consiste nella ricerca di una buona (cioè naturale) nozione. di sottovarietà regolari e nello studio delle loro proprietà. In questo seminario presentiamo alcuni capitoli di questo programma secondo le linee di una monografia scritta in collaborazione con Raul Serapioni e Francesco Serra Cassano, Some topics of Geometric Measure Theory in Carnot Groups (in preparazione).

2022
26 Aprile
Irina Mitrea (Department of Mathematics, Temple University)
A Sharp Divergence Theory with Non-Tangential Traces

seminario di analisi matematica

The Integration by Parts Formula, which is equivalent with the Divergence Theorem, is one of the most basic tools in Analysis. Originating in the works of Gauss, Ostrogradsky, and Stokes, the search for an optimal version of this fundamental result continues through this day and these efforts have been the driving force in shaping up entire subbranches of mathematics, like Geometric Measure Theory. In this talk I will review some of these developments (starting from elementary considerations to more sophisticated versions) and I will discuss recents result regarding a sharp divergence theorem with non-tangential traces. This is joint work with D. Mitrea and M. Mitrea.

2022
07 Aprile
Federica Sani (Università di Modena e Reggio Emilia).
Extremal functions for Adams inequalities with Navier boundary conditions

seminario di analisi matematica

We prove the existence of extremal functions for second order Adams inequalities with Navier boundary conditions on balls in R^n in any dimension n>3. The proof is based on a symmetrization argument and the ideas introduced by Carleson and Chang to prove the existence of extremal functions in the first order case, i.e. extremal functions for the Trudinger-Moser inequality on balls. We also derive a supercritical version of this result for spherically symmetric functions.

2022
24 Marzo
Ermanno Lanconelli
Il ''problema di Dirichlet'' per l'equazione del calore: un metodo elementare

seminario di analisi matematica

Una delle maggiori difficoltà tecniche, nella risoluzione col metodo di Perron del ''Problema di Dirichlet'' per l'equazione del calore, è la costruzione di una base di aperti della topologia euclidea sui quali quel problema è risolubile. Nel seminario verrà dimostrato che la difficoltà si può superare in modo elementare, utilizzando un argomento tratto dalla teoria dei polinomi calorici, il principio del massimo e un semplice risultato di algebra lineare.

2022
17 Marzo
Cyril Letrouit (ENS Paris)
Propagation of singularities in subelliptic PDEs

seminario di analisi matematica

In this talk, we consider the wave equation where the Laplacian is replaced by a sub-Laplacian (also called ``Hörmander sum of square''), which is an hypoelliptic operator. We handle the problem of describing the propagation of singularities in such equations : the main new phenomenon that we describe is that singularities can propagate along abnormal curves at any speed between 0 and 1. This general result extends an idea due to R. Melrose, and we then illustrate it on an example, the Martinet case, following a joint work with Y. Colin de Verdière. Our statements are part of a classical/quantum correspondance between sub-Riemannian geometry (on the classical side) and the hypoelliptic operator (on the quantum side), which is also helpful to interpret results in control theory and spectral theory of hypoelliptic operators.

2022
10 Marzo
Claudia Lederman, University of Buenos Aires, Argentina
Free boundary regularity for a one-phase problem with non-standard growth

seminario di analisi matematica

We consider viscosity solutions to a one-phase free boundary problem for a nonlinear elliptic PDE with non-zero right hand side. We obtain regularity results for solutions and their free boundaries. The operator under consideration is a model case in the class of partial differential equations with non-standard growth. This type of operators have been used in the modelling of non-Newtonian fluids, such as electrorheological or thermorheological fluids, also in non-linear elasticity and image reconstruction. We also obtain some new results for the governing operator that are of independent interest. This is joint work with Fausto Ferrari (University of Bologna, Italy)

2022
24 Febbraio
Antonio J. Fernandez
Desingularization of vortices for the generalized SQG equations

seminario di analisi matematica

We consider the generalized inviscid surface-quasigeostrophic equations (gSQG) and analyse the existence of a smooth compactly supported solution to the (gSQG) which is concentrated around N moving vortices. The result we discuss could be understood as the extension to the case of the (gSQG) of the seminal result of Marchioro and Pulvirenti concerning the bi-dimensional incompressible Euler equations. However, the information about the dynamic behaviour and the shape of the constructed solution that we obtain is much more precise than the obtained by Marchioro and Pulvirenti. The talk is based on a joint work with Manuel del Pino.

2022
24 Febbraio
Antonio J. Fernandez
Desingularization of vortices for the generalized SQG equations

seminario di analisi matematica

We consider the generalized inviscid surface-quasigeostrophic equations (gSQG) and analyse the existence of a smooth compactly supported solution to the (gSQG) which is concentrated around N moving vortices. The result we discuss could be understood as the extension to the case of the (gSQG) of the seminal result of Marchioro and Pulvirenti concerning the bi-dimensional incompressible Euler equations. However, the information about the dynamic behaviour and the shape of the constructed solution that we obtain is much more precise than the obtained by Marchioro and Pulvirenti. The talk is based on a joint work with Manuel del Pino.

2022
17 Febbraio
Fabiana Leoni (Sapienza Università di Roma)
New concentration phenomena for radial solutions of fully nonlinear elliptic equations

seminario di analisi matematica

We present recent results about radial solutions of a class of fully nonlinear elliptic Dirichlet problems posed in a ball, driven by the extremal Pucci's operators and provided with power zero order terms. We show that a new critical exponent appears, related to the existence or nonexistence of sign-changing solutions. Furthermore we analyze the new concentration phenomena occurring as the exponents approach the critical values. Based on joint works with A. Iacopetti, G. Galise and F. Pacella.

2022
27 Gennaio
Gregorio Chinni
On the regularity of solutions and of analytic vectors for ``sums of squares"

seminario di analisi matematica

We present some results concerning the local and global regularity of the solutions for some classes/models of sums of squares of vector fields with real-valued real analytic coefficients of Hörmander type. Moreover we also illustrate a result concerning the microlocal Gevrey regularity of analytic vectors for operators sums of squares of vector fields with real-valued real analytic coefficients of Hörmander type, thus providing a microlocal version, in the analytic category, of a result due to M. Derridj.

2021
16 Dicembre
Gianmarco Giovannardi (Università di Trento)
The Bernstein problem for Euclidean Lipschitz surfaces in the sub-Finsler Heisenberg group H^1.

seminario di analisi matematica

We shall prove that in the first Heisenberg group with a sub-Finsler structure, a complete, stable, Euclidean Lipschitz surface without singular points is a vertical plane. This is joint work with Manuel Ritoré.

2021
13 Dicembre
Nikolaos Chalmoukis
Interpolation by analytic functions in Sobolev spaces

seminario di analisi matematica

We shall present a characterization of simply interpolating sequences in the Dirichlet space. The same characterization is conjectured to hold in all complete Nevanlinna Pick spaces but the problem remains open despite recent progress. Finally, we are going to discuss some variants of the classical interpolation problem, such as random interpolation. This is a field where numerous questions remain open. Extended abstract: https://site.unibo.it/complex-analysis-lab/en/news-1/piniseminarabstract.pdf/@@download/file/PiniSeminarAbstract.pdf

2021
28 Ottobre
Lorenzo Zanelli (Dipartimento di Matematica, Universita` di Padova)
Phase space Analysis of Wick operators on Bargmann space with applications to discrete NLS

seminario di analisi matematica

We show a link between weighted Hilbert-Schmidt norms of Wick operators on Bargmann space and $L^2$-norm of Wick symbols with respect to a class of measures on the complex phase space. As an application, we derive the flow of discrete NLS equations by the mean field asymptotics of a many body quantum model for $N$ interacting particles as $N$ becomes large.

2021
06 Ottobre
Sergio Polidoro
Formule di media per soluzioni classiche di equazioni uniformemente paraboliche e generalizzazioni a gruppi di Lie

seminario di analisi matematica

Dimostriamo formule di media, di superficie e di volume, per soluzioni classiche di equazioni paraboliche in forma di divergenza sotto ipotesi naturali sulla regolarità dei coefficienti. La dimostrazione si basa sulle proprietà usuali della soluzione fondamentale delle equazioni paraboliche, su un teorema di divergenza generalizzato e su un preciso risultato dovuto a Dubovickii sulla regolarità degli insiemi di livello delle funzioni C^1. Discuteremo infine la generalizzazione di queste formule di media al contesto degli operatori subellittici nei gruppi di Carnot. I risultati di questo seminario sono stati ottenuti in collaborazione con Diego Pallara ed Emanuele Malagoli.

2021
24 Giugno
Shirsho, Mukherjee
On minimax characterization in non-linear eigenvalue problems

seminario di analisi matematica

In this talk, we shall exhibit a mini-max characterization of the second eigenvalue of the p-Laplacian operator on p-quasi-open sets, using a construction based on minimizing movements on non-linear gradient flows. The following outline shall be presented: the notion of non-linear eigenvalues and their properties, the statement of the characterization, the notion of Quasi-open sets, and a sketch of the proof of the theorem. This is based on a joint work with Nicola Fusco and Yi Zhang.

2021
17 Giugno
Giuseppe Savarè, Università Bocconi, Milano
Optimal Transport: a brief overview

seminario di analisi matematica

The talk will introduce the main concepts and tools of Optimal Transport between probability measures and its recent extensions to the unbalanced case, involving entropic regularizations. A few applications will also be discussed.

2021
10 Giugno
Nicolò Forcillo
Regularity of the free boundary in the one-phase Stefan problem: a recent approach

seminario di analisi matematica


2021
03 Giugno
F. Santambrogio (Université Claude Bernard - Lyon 1)
News from the JKO scheme for linear and non-linear diffusion PDEs as Wasserstein gradient flows

seminario di analisi matematica

I will start the talk by recalling the notion of gradient flow in its easiest occurrence: the evolution equation x'(t)=-grad F(x(t)) in the Euclidean space. In particular, the focus will be on the implicit Euler scheme as a sequence of iterated minimization problems. I will then move to a more involved setting, where the point x is replaced by a probability density ρ evolving in the space of probabilities endowed with the so-called Wasserstein distance, induced by optimal transport. For suitable choices of the functional F one can recover linear diffusion PDEs (heat and Fokker-Planck equations) as well as non-linear ones (porous medium, fast diffusion, models for crowd motion). The iterated minimization scheme is called in this case JKO scheme (from Jordan-Kinderlehrer-Otto). After explaining why this scheme heuristically provide the desired equation at the limit, I will show how its optimality conditions can be exploited to prove estimates on its solutions, in particular BV, Sobolev and Lipschitz bounds. Lipschitz estimates can also be interpreted as bounds on the maximal displacement of each particle in the optimal transport map, and have a numerical interest, which I will discuss in two examples, where a potential drift is coupled either with linear diffusion or with a pressure effect due to density constrained in crowd motion.

2021
20 Maggio
Veronique FISCHER
Towards semi-classical analysis for sub-elliptic operators

seminario di analisi matematica

In this talk, I will discuss the development of semi-classical analysis for sub-elliptic operators such as sub-Laplacians. For an elliptic operator, this is well understood as the tools and methods to study e.g. quantum ergodicity or Schrödinger equations have become well established over the past fifty years. They rely on the pseudo-differential theory, and in the elliptic case the space of principal symbols is commutative. The aim of this talk is to present my approach to define similar tools for sub-Laplacians, leading to more non-commutative concepts.

2021
13 Maggio
Berardo Ruffini
Optimal design problems with repulsive term

seminario di analisi matematica

Some new ideas in Calculus of Variation and Geometric Measure Theory allowed, in the last decade, to revisit from a precise mathematical point of view some physical models. Instances of such models are the Lord Rayleigh model of charged liquid drops in electrowetting, the liquid drop model by Gamow to describe nuclear fissions, the Hartree equations in atomic physics. In the seminar I will give a brief overview on such results. Later I will focus on recent results about some of those topics. The topic of the talk is partially based upon works in collaboration with M. Goldman, D. Mazzoleni, C.B. Muratov and M. Novaga.

2021
06 Maggio
Matteo Novaga (Università di Pisa)
Some remarks on nonlocal curvature flows

seminario di analisi matematica

I will introduce the nonlocal curvature flows, discussing existence, uniqueness and stability of solutions. In the particular case of the fractional mean curvature flow, I will also describe the long time behaviour of graphical solutions and some issues related to the formation of singularities.

2021
29 Aprile
Maria Carla Tesi
The synergistic interplay between two proteins: a mathematical model for Alzheimer's disease

seminario di analisi matematica

There is currently a great deal of interest in the scientific community in investigating the effects of the synergistic interplay of Amyloid beta and tau on the dynamics of Alzheimer’s disease. I will present a mathematical model for the onset and progression of Alzheimer’s disease based on transport and diffusion equations for the two proteins. In the model neurons are treated as a continuous medium and structured by their degree of mal- functioning. Three different mechanisms are assumed to be relevant for the temporal evolution of the disease: i) diffusion and agglomeration of soluble Amyloid beta, ii) effects of misfolded tau protein and iii) neuron-to- neuron prion-like transmission of the disease. These processes are modelled by a system of Smoluchowski equations for the Amyloid beta concentration, an evolution equation for the dynamics of tau protein and a kinetic-type transport equation for the distribution function of the degree of malfunctioning of neurons. The latter equation contains an integral term describing the random onset of the disease as a jump process localized in particularly sensitive areas of the brain. I will explain in detail the structure of the model and give a hint of the main results obtained and the techniques used for the purpose. Eventually I will also show the output of some numerical simulations, of some significance even if performed in an over-simplified 2D geometry.

2021
09 Marzo
Alessandro Iacopetti, Università di Milano, La Statale
New regularity and existence results for the prescribed mean curvature equation in the Lorentz-Minkowski space

seminario di analisi matematica

In this talk we present some recent results concerning the regularity of the unique weak solution vanishing at infinity of the prescribed mean curvature equation in the Lorentz-Minkowski space for spacelike hypersurfaces, when the mean curvature belongs to $L^p(R^N)$, with $p>N$. This equation is also known as the ``Born-Infeld'' equation, as it comes from the nonlinear model of electromagnetism introduced by M. Born and L. Infeld, but it also plays a crucial role in Relativity. In the first part of the talk we will show a new gradient estimate for smooth solutions of the prescribed mean curvature equation and prove that, under our assumptions, the unique minimizer of the Born-Infeld energy, which is a priori only Lipschitz continuous, is actually a strictly spacelike weak solution of class $W^{2,p}$. In the second part the we will discuss some other related results concerning the existence of spacelike radial graphs of prescribed mean curvature and some open problems. These results are collected in a series of joint works with Prof. D. Bonheure (Université Libre de Bruxelles).

2021
04 Marzo
Nicola Abatangelo, Goethe-Universität Frankfurt am Main
Higher-order fractional Laplacians: An overview

seminario di analisi matematica

We will present a series of results regarding the behaviour of solutions to boundary value problems driven by non-integer powers of the Laplacian operator. Special attention will be paid to the failure of maximum principles and its consequences.

2020
19 Novembre
Maria Manfredini
Intrinsic Taylor formula in fractional Holder space

seminario di analisi matematica

We consider a class of non-local ultraparabolic Kolmogorov operators and we study suitable fractional Holder spaces that take into account the intrinsic sub-riemannian geometry induced by the operator. We prove a characterization relating the regularity along the vector fields to the existence of appropriate instrinsic Taylor formulas which extends in the non-local context the characterization given in the diffusive setting.

2020
06 Ottobre
Carlo Mariconda
The basic problem of the calculus of variations: new range of validity of the Du Bois - Reymond equation and applications to regularity

seminario di analisi matematica


2020
02 Aprile
Carlo Mariconda
TBA

seminario di analisi matematica

TBA

2020
26 Marzo
Karlheinz Groechenig
Totally positive functions, sampling, and Gabor frames

seminario di analisi matematica

Totally positive functions play an important role in approximation theory and statistics. I will discuss some recent applications of totally positive functions in sampling theory and time-frequency analysis. At this time totally positive functions are the only functions for which optimal results for sampling in shift-invariant spaces and for Gabor frames have been proved.

2020
30 Gennaio
Matteo Franca
A dynamical system approach to the scalar curvature equation: multiplicity results.

seminario di analisi matematica

In this talk we illustrate results concerning radial positive solutions of semi-linear elliptic equations such as $$\Delta u + k(|x|) u^{q-1}=0 \qquad \qquad \qquad (1)$$ where $x \in \mathbb{R}^n$, $n>2$, $k(|x|)>0$, and its generalization to the $p$-Laplace case. We focus in particular on the critical case $q=2^*=\frac{2n}{n-2}$. Our goal is to find conditions on $k$ ensuring existence and multiplicity of ground states with fast decay, i.e. solutions $u(x)$ defined and positive in the whole of $\mathbb{R}^n$ and decaying as $|x|^{-(n-2)}$ for $|x|$ large. Using Fowler transformation we pass from (1) to a two dimensional dynamical system so that we can apply phase plane techniques such as invariant manifold theory, shooting, Melnikov theory. In particular the search of ground states with fast decay is translated on the search of homoclinic trajectories.

2020
16 Gennaio
Guido De Philippis
Regularity of the free boundary for the two-phase Bernoulli problem.

seminario di analisi matematica

I will illustrate a recent result obtained in collaboration with B. Velichkov and L. Spolaor concerning the regularity of the free boundaries in the two phase Bernoulli problems. The new point is the analysis of the free boundary close to branch points, where we show that it is given by the union of two C^1 graphs. This complete the analysis started by Alt Caffarelli Friedman in the 80’s.

2019
12 Dicembre
Nicola Arcozzi
Disuguaglianze differenziali e disuguaglianze integrali

seminario di analisi matematica

Il filo di questo seminario, del tutto espositivo, segue, in una particolare direzione, la relazione che intercorre tra disuguaglianze differenziali e integrali: a partire dalla nota disuguaglianza di Jensen (e, tempo permettendo, gli spazi di Orlicz), attraverso classici argomenti di subarmonicità nello studio di alcuni integrali singolari, quindi il metodo di Burkholder per stime di operatori su spazi di martingale, e arrivare infine al metodo delle funzioni di Bellman di Nazarov, Treil e Volberg, che ha le sue radici nella teoria del controllo stocastico ottimale.

2019
05 Dicembre
Chiara Guidi
Characterization of the Palais-Smale sequences for the fractional CR Yamabe functional

seminario di analisi matematica

In this talk we consider the functional whose critical points are solutions of the fractional CR Yamabe-type equation on the CR sphere. Due to the lack of compactness for the associated critical Sobolev embedding, the functional does not satisfy the Palais-Smale condition. By adapting a classical arguments by Struwe and by making use of some recent commutator estimates, which allow us to deal with our non-local setting, we obtain a characterization of the Palais-Smale sequences. Then, as an application, we prove a multiplicity result for the related equation. This is joint work with A.Maalaoui and V.Martino.

2019
23 Ottobre
Dario Mazzoleni
Optimization results for the higher eigenvalues of the p-Laplacian

seminario di analisi matematica

In this talk we study the existence of an optimal set for the minimization of the $k$-th variational eigenvalue of the $p$-Laplacian among $p$-quasi open sets of fixed measure included in a box of finite measure. An analogous existence result is obtained for eigenvalues of the $p$-Laplacian associated with Schr\"odinger potentials. In order to deal with these nonlinear shape optimization problems, we develop a general approach which allows to treat the continuous dependence of the eigenvalues of the $p$-Laplacian associated with sign-changing capacitary measures under $\gamma$-convergence.

2019
16 Ottobre
Pierre Bousquet (U. Tolosa)
ON THE ORTHOTROPIC LAPLACIAN

seminario di analisi matematica

We present some new regularity results for the orthotropic harmonic functions, which are the minimizers of a egenerate and anisotropic variant of the Dirichlet functional. These results have been obtained in collaboration with L. Brasco (Ferrara), V. Julin (Jyvaskyla), C. Leone (Naples) and A. Verde (Naples).

2019
04 Luglio
Daniela De Silva
Viscosity solutions approach to variational problems

seminario di analisi matematica

In this talk we discuss some extensions of the classical Krylov-Safonov Harnack inequality. After reviewing the standard regularity theory, we will introduce a weaker notion of viscosity solutions. The novelty is that we consider functions that do not necessarily satisfy an infinitesimal equation but rather exhibit a two-scale behavior. Roughly, our viscosity solutions satisfy comparison in a neighborhood of a touching point whose size depends on the properties of the test functions. As an application, we recover the C^{1,\alpha} estimates of Almgren and Tamanini for quasi-minimizers of the perimeter functional. We also establish the regularity of the free boundary for almost minimizers of one-phase type problems.

2019
04 Luglio
Ovidiu Savin, Columbia University, New York
The singular set in the fully nonlinear obstacle problem

seminario di analisi matematica

For the Obstacle Problem involving a convex fully nonlinear elliptic operator, we show that the singular set of the free boundary stratifies. The top stratum is locally covered by a $C^{1,\alpha}$-manifold, and the lower strata are covered by $C^{1,\log^\eps}$-manifolds. This essentially recovers the regularity result obtained by Figalli-Serra when the operator is the Laplacian.

2019
04 Giugno
Xavier Cabré, ICREA and Universitat Politècnica de Catalunya (Barcelona)
A gradient estimate for nonlocal minimal graphs

seminario di analisi matematica

The talk will be concerned with s-minimal surfaces, that is, hypersurfaces of R^n with zero nonlocal mean curvature. These are the equations associated to critical points of the fractional s-perimeter. We will present a recent result in collaboration with M. Cozzi in which we establish, in any dimension, a gradient estimate for nonlocal minimal graphs. It leads to their smoothness, a result that was only known for n=2 and 3 (but without a quantitative bound); in higher dimensions only their continuity had been established. We will also present a work with E. Cinti and J. Serra in which we prove that half spaces are the only stable s-minimal cones in R^3 for s sufficiently close to 1.

2019
16 Maggio
Annalisa Baldi
Poincaré and Sobolev inequalities for differential forms on Euclidean spaces and Heisenberg groups.

seminario di analisi matematica

In this talk we present some recent results obtained in collaboration with B. Franchi and P. Pansu about Poincaré and Sobolev inequalities in Heisenberg groups (some results are new also for Euclidean spaces). For $L^p$, $p>1$, the estimates are consequence of singular integral estimates. I would like to concentrate the seminar, in particular, to the limiting case $L^1$, where the exterior Rumin-differential of a differential form is measured in $L^1$ norm. Unlike for $L^p$, $p>1$, the estimates are doomed to fail in top degree. In the limiting case, the singular integral estimates are replaced with inequalities which go back to Bourgain-Brezis and Lanzani-Stein in Euclidean spaces, and to Chanillo-Van Schaftingen and Baldi-Franchi-Pansu in Heisenberg groups.

2019
09 Maggio
Ermanno Lanconelli
Mean value formulas and Liouville theorems for linear second order PDEs

seminario di analisi matematica

We present several Mean Value formulas for solutions to linear second order PDEs endowed with smooth ''local fundamental solutions''. We then show how these formulas can be used to obtain Liouville Theorems for entire solutions. Our formulas are, in general, weighted average formulas. The relevant weights are ''densities with the mean value property'' a notion playing a central role in rigidity and stability problems. The results we present, related to the Mean value formulas, are obtained in collaboration with Giovanni Cupini. The ones related to the Liouville Theorems are joint works with Alessia Kogoj.

2019
11 Aprile
Menita Carozza
On weakly monotone functions
The notion of weakly monotone functions was introduced, in the setting of Sobolev spaces, by J.Manfredi, in connection with the analysis of the regularity of maps of finite distortion appearing in the theory of nonlinear elasticity. We propose a criterion for the continuity of weakly monotone functions in terms of the decreasing rearrangement of their gradient. We also prove the continuity of weakly monotone functions whose gradient is in suitable rearrangement-invariant spaces. In particular, weakly monotone functions with gradient belonging to an Orlicz space or to a Lorentz space are discussed. These results are contained in joint works with Andrea Cianchi.

2019
04 Aprile
Stefano Biagi
Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators

seminario di analisi matematica

Maximum Principles on unbounded domains play a crucial role in several problems related to linear second-order PDEs of elliptic and parabolic type. In this seminar we consider a class of sub-elliptic operators L in R^N and we establish some criteria for an unbounded open set to be a Maximum Principle set for L.

2019
21 Marzo
Antonio Vitolo, Università di Salerno
Maximum principles with low ellipticity

seminario di analisi matematica


2019
06 Marzo
Andrea Cosso
McKean-Vlasov stochastic control and Hamilton-Jacobi-Bellman equations on Wasserstein space

seminario di probabilità


2019
28 Febbraio
Claudia Bucur, Università Cattolica del Sacro Cuore
Behaviour of nonlocal sets for small values of the fractional parameter

seminario di analisi matematica


2018
06 Dicembre
Giorgio Tortone, Università degli studi di Torino
On the nodal set of solutions to degenerate or singular elliptic equations with an application to s-harmonic functions

seminario di analisi matematica

 
We will discuss the geometric-theoretic analysis of the nodal set of solutions to degenerate or singular equations involving a class of operators including L_a = div(|y|^a \nabla), with -1<a<1 and their perturbations. As they belong to the Muckenhoupt class A_2, these operators appear in the seminal works of E. Fabes, C. Kenig, D. Jerison and R. Serapioni and have recently attracted a lot of attention in the last decade due to their link to the localization of the fractional Laplacian via the extension in one more dimension. Our goal is to develop a complete theory of the stratification properties for the nodal set of solutions of such equations in the spirit of the seminal works of R. Hardt, L. Simon, Q. Han and F.-H. Lin, giving several applications in the context on solutions to non-local elliptic equations with fractional Diffusions. This is a joint work with Y. Sire and S. Terracini.

2018
15 Novembre
Luca Martinazzi
News on the Moser-Trudinger inequality

seminario di analisi matematica

The existence of critical points for the Moser-Trudinger inequality for large energies has been open for a long time. We will first show how a collaboration with G. Mancini allows to recast the Moser-Trudinger inequality and the existence of its extremals (originally due to L. Carleson and A. Chang) under a new light, based on sharp energy estimate. Building upon a recent subtle work of O. Druet and P-D. Thizy, in a work in progress with O. Druet, A. Malchiodi and P-D. Thizy, we use these estimates to compute the Leray-Schauder degree of the Moser-Trudinger equation (via a suitable use of the Poincaré-Hopf theorem), hence proving that for any bounded non-simply connected domain the Moser-Trudinger inequality admits critical points of arbitrarily high energy. In a work in progress with F. De Marchis, O. Druet, A. Malchiodi and P-D. Thizy, we expect to use a variational argument to treat the case of a closed surface.

2018
08 Novembre
Stefano Vita
On s-harmonic functions on cones

seminario di analisi matematica

We deal with non negative s-harmonic functions in a cone C of R^n (with vertex at the origin), which satisfy 0-Dirichlet boundary conditions in the complement of the cone. We consider the case when $s$ approaches $1$, wondering whether solutions of the problem do converge to harmonic functions in the same cone or not. Surprisingly, the answer will depend on the opening of the cone through an auxiliary eigenvalue problem on the upper half sphere. These conic functions are involved in the study of the nodal regions in the case of optimal partitions and other free boundary problems and play a crucial role in the extension of the Alt-Caffarelli-Friedman monotonicity formula to the case of fractional diffusions.

2018
11 Ottobre
Xiao Zhong (Università di Helsinki)
On the Euler-Lagrange equation of a functional by Pólya and Szegö
I will talk about a conjecture of Pólya and Szegö on minimal electrostatic capacity sets in convex shape optimization. The functional, associated to the conjecture, involves capacity and perimeter. We will focus on the generalized solutions of the corresponding Euler-Lagrange equation and talk about recent joint work with Nicola Fusco.

2018
07 Giugno
Davide Guidetti
On maximal regularity for the Cauchy-Dirichlet mixed parabolic problem with fractional time derivative

seminario di analisi matematica

In this seminar we illustrate some results of maximal regularity for the Cauchy-Dirichlet mixed problem, with a fractional time derivative of Caputo type in spaces of continuous and Hölder continuous functions. In questo seminario presentiamo alcuni risultati di regolarità massimale per il problema misto di Cauchy-Dirichlet, con una derivata temporale frazionaria di Caputo, in spazi di funzioni continue e hölderiane.

2018
29 Maggio
Hitoshi Ishii, Tsuda University, Japan
The vanishing discount problem for fully nonlinear degenerate elliptic PDEs

seminario di analisi matematica

I discuss an approach, based on generalized Mather measures, to the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations. Under mild assumptions, we introduce viscosity Mather measures for such PDEs, which are natural extensions of Mather measures, originally due to J. Mather. Using the viscosity Mather measures, we can show that the whole family of solutions $v^\lambda$ of the discounted problem, with the discount factor $\lambda$, converges to a solution of the ergodic problem as $\lambda$ goes to 0. This is based on joint work with Hiroyoshi Mitake (Hiroshima University) and Hung V. Tran (University of Wisconsin, Madison).

2018
17 Maggio
Carlo Sinestrari
Formazione di singolarità nel moto secondo la curvatura media frazionaria

seminario di analisi matematica

Nel 2009, Caffarelli, Roquejoffre e Savin hanno introdotto una nozione non locale di perimetro di insiemi, detto perimetro frazionario. Dalla variazione prima del perimetro si ottiene la curvatura media frazionaria di un insieme, che è definita da un operatore integrale con nucleo singolare. Da allora, vari autori hanno studiato queste nozioni, ottenendo ad esempio proprietà di regolarità per superfici minime non locali, esistenza di superfici di tipo Delaunay a curvatura frazionaria costante, e disuguaglianze isoperimetriche. Più recentemente, è stato considerato il moto di superfici secondo la curvatura media frazionaria, che è il flusso gradiente del perimetro non locale, ottenendo risultati di esistenza e unicità per soluzioni deboli e proprietà di invarianza. Dopo aver richiamato queste proprietà, ci soffermeremo su un risultato in collaborazione con E. Cinti ed E. Valdinoci, che dimostra l'esistenza di superfici che sviluppano singolarità di tipo "collo di bottiglia" (neckpinch). E' interessante notare che, come conseguenza della natura non locale della curvatura frazionaria, tali singolarità si sviluppano in qualunque dimensione, inclusa quella orrispondente al caso di curve nel piano. In questo aspetto l'evoluzione si differenzia da quella classica, dove le curve si contraggono a un punto senza sviluppare singolarità in base al teorema di Grayson.

2018
10 Maggio
Francesca Prinari
Level convessita' e distanze intrinsiche nei problemi variazionali in L^\infty

seminario di analisi matematica

In questo seminario, dopo aver introdotto la nozione di level convessita' ed il ruolo che essa riveste nei problemi di Calcolo delle Variazioni in L^\infty, si studiera' l'inviluppo semicontinuo di un funzionale della forma $$F(u)=\supess_{\Omega} f(x,Du(x))$$ su $W^{1,\infty}(\Omega)$ rispetto la topologia debole* e si dimostrera' che esso soddisfa la proprieta' di level convessita'. A tal fine si rappresenteranno i sottolivelli del funzionale rilassato per mezzo di opportune pseudo-distanze associate al funzionale $F$.

2018
03 Maggio
Angelo Favini
Degenerate Differential Problems with Fractional Derivatives.

seminario di analisi matematica


2018
19 Aprile
Giulio Ciraolo
Stime quantitative per ipersuperfici a curvatura media quasi costante

seminario di analisi matematica

Discuteremo alcune versioni quantitative del Teorema di Alexandrov della bolla di sapone, che afferma che le sfere sono le sole ipersuperfici chiuse embedded a curvatura media costante. In particolare, considereremo ipersuperfici con curvatura media vicina ad una costante e descriveremo in maniera quantitativa la vicinanza ad una singola sfera o ad una collezione di sfere tangenti di raggio uguale in termini dell'oscillazione della curvatura media. Inoltre considereremo il problema analogo in ambito nonlocale, mostrando come l'effetto nonlocale implichi una maggiore rigidità del problema e prevenga la formazione di più bolle.

2018
05 Aprile
Matteo Focardi (U. Firenze)
The measure and the structure of the free boundary in the lower dimensional obstacle problem

seminario di analisi matematica

In this talk I present the main results of a recent paper in collaboration with E. Spadaro (U. Roma La Sapienza) on the regularity of the free boundary for a class of lower dimensional obstacle problems, including the classical scalar Signorini problem. We prove the first results concerning the global structure of the free boundary, in particular showing its local finiteness and its rectifiability.

2018
23 Marzo
Lorenzo Brasco (Università di Ferrara)
The Faber-Krahn inequality

seminario di analisi matematica

Among N-dimensional open sets with given measure, balls (uniquely) minimize the first eigenvalue of the Laplacian with homogeneous Dirichlet boundary conditions. We review this classical result and discuss some of its applications. Then we show how this can be enhanced by means of a quantitative stability estimate. The resulting inequality, first conjectured by Nadirashvili and Bhattacharya & Weitsman, is sharp. The results presented are contained in a paper in collaboration with Guido De Philippis and Bozhidar Velichkov.

2018
15 Marzo
Giovanni Cupini
Everywhere regularity of vectorial minimizers of some non-convex functionals

seminario di analisi matematica

The convexity of the integrand of a functional of the calculus of variations is equivalent to the lower semicontinuity of the functional in the scalar case, but it is only a sufficient condition in the vectorial case. So, it is not satisfied by many interesting examples to which the existence theorems apply. Moreover, the convexity of the integrand turns out to be a too strong and unrealistic assumption in applications, as for instance in mathematical models in nonlinear elasticity (Ball 1977). In the vectorial framework more appropriate and weaker conditions than the convexity are the polyconvexity and the quasiconvexity. Under these assumptions, many results were proved concerning the partial regularity of minimizers (regularity on open sets of full measure), but the results concerning the everywhere regularity are very few and mainly in low dimensions (n=N=2). We will discuss recent everywhere regularity results of vectorial minimizers for some classes of polyconvex and quasiconvex functionals (n,N >2) obtained in collaboration with F. Leonetti and E. Mascolo (local boundedness) and with them and M. Focardi (Holder continuity). The proofs rely on the power and elegant (typically scalar) method by De Giorgi (1957).

2018
08 Marzo
Pavel Mozolyako
Carleson measures for the Dirichlet space on the polydisc
The Dirichlet space on the polydisc consists of analytic functions defined on the cartesian product of n-copies of a disc, having finite Sobolev norm. In the one-dimensional case (d = 1) the Carleson measures were first described by Stegenga (’80) in terms of capacity, further development was achieved in papers by Arcozzi, Rochberg, Sawyer, Wick and others. Following Arcozzi et al. we consider the equivalent problem in the discrete setting - characterization of trace measures for the Hardy operator on the polytree. For d = 2 we present a description of such measures in terms of bilogarithmic capacity (which, in turn, gives the description of Carleson measures for the Dirichlet space on the bidisc in the sense of Stegenga). We also discuss some arising combinatorial problems. This talk is based on joint work with N. Arcozzi, K.-M. Perfekt, G. Sarfatti.

2018
22 Febbraio
Scott Rodney
Poincaré-Sobolev Inequalities and the p-Laplacian

seminario di analisi matematica


2018
15 Febbraio
Marco Bramanti
La tecnica della funzione massimale sharp nelle stime a priori W^{2,p} per operatori non variazionali

seminario di analisi matematica


2018
08 Febbraio
Sandra Lucente
Esponenti critici e dove trovarli

seminario di analisi matematica

In this talk I will present different semilinear wave-type problems with time-variable coefficients. Main discussion will concern the influence of such coefficients on the critical exponents which characterize the equation. The analysis of global existence and blow-up below or above this critical exponent will follows.

2018
01 Febbraio
Roberto Monti
Il problema della regolarità delle geodetiche per le distanze di controllo.

seminario di analisi matematica

Illustreremo una serie di risultati in collaborazione con vari coautori sul problema della regolarità delle curve minime per la lunghezza negli spazi di Carnot-Caratheodory. Discuteremo l'esistenza di tangenti in ogni punti a valcuni risultati algebrici sulle cosiddette curve abnormali.

2017
14 Dicembre
Fabiana Leoni, Università di Roma "La Sapienza"
Asymptotic analysis in the ball for almost critical fully nonlinear elliptic equations

seminario di analisi matematica


2017
07 Dicembre
Pieralberto Sicbaldi, Università di Granada e Université d'Aix-Marseille
Geometria dei problemi ellittici sovradeterminati

seminario di analisi matematica


2017
23 Novembre
Francis NIER
Boundary conditions for Kramers-Fokker-Planck operators

seminario di analisi matematica

I will present a class of boundary conditions for Kramers-Fokker-Planck operators which guarantees subelliptic estimates similar to the whole space problem.

2017
15 Giugno
Davide Guidetti
Derivate temporali frazionarie ed equazioni di evoluzione

seminario di analisi matematica

 
In questo seminario introduciamo le derivate frazionarie di Riemann-Liouville e di Caputo, con alcune delle loro principali proprietà. Concludiamo illustrando alcuni risultati di regolarità massimale per problemi misti al contorno, in cui compaiono tali derivate.

2017
18 Maggio
Yannick Sire (Johns Hopkins University)
Fractional Poincaré inequalities on manifolds with finite total Q-curvature

seminario di analisi matematica

We establish new fractional Poincaré inequalities encoding geometry of conformally flat manifolds with finite total Q-curvature. The method of proof is based on some improvement of the standard Poincare inequality and harmonic analysis techniques. We will give a description of the underlying geometry and in particular the role of the Q-curvature.

2017
11 Maggio
Paolo Albano
On the homogeneous Dirichlet problem for the subelliptic eikonal equation

seminario di analisi matematica

abstract: We consider the subelliptic eikonal equation, i.e. the eikonal equation associated with a family of (real) smooth vector fields satisfying the Hoermander bracket generating condition on a neighborhood of an open bounded set with smooth boundary. We study the regularity and the singularities of the viscosity solution of the homogeneous Dirichlet problem for such an equation.

2017
08 Maggio
Rolando Magnanini
Alexandrov, Serrin, Weinberger, Reilly: symmetry and stability

seminario di analisi matematica

Il Soap Bubble Theorem (SBT) stabilisce che una superficie compatta con curvatura media costante è una sfera. Per dimostrare questo risultato, A. D. Alexandrov ha inventato il suo principio di riflessione, che è stato in seguito perfezionato da J. Serrin nel metodo dei piani mobili, per ottenere la simmetria radiale per una classe di problemi sovra-determinati. H. F. Weinberger ha fornito una dimostrazione del risultato di Serrin basata su alcune identità e disuguaglianze integrali. R. C. Reilly ha infine fatto vedere come il metodo di Weinberger può essere usato per ottenere un'altra dimostrazione del SBT. Nel mio seminario, seguendo le orme di Weinberger e Reilly, farò vedere come i due risultati di simmetria discendano da due identità integrali per la rigidità torsionale di una sbarra. Le due identità saranno poi usate per ottenere risultati di stabilità della configurazione sferica nei due problemi ed in altri problemi analoghi.

2017
04 Maggio
Erika Battaglia
The Harnack inequality for several classes of sub-elliptic operators.

seminario di analisi matematica

In this seminar some recent results concerning Harnack inequalities will be presented for several classes of sub-elliptic operators. We will start by considering a class of sub-elliptic operators, in divergence form, with low-regular coefficients under global doubling and Poincaré assumptions; for these operators a non-homogeneous invariant Harnack inequality will be shown. As a consequence, we will prove the solvability of the Dirichlet problem (in a suitable weak sense). In the second part, we will consider a class of hypoelliptic non-Hormander operators for which we have been able to construct a Green function; with a completely different approach with respect to the case of doubling metric spaces, we will conclude by showing (by means of techniques of Potential Theory) how the solvability of the Dirichlet problem has been a fundamental tool in order to prove a homogeneous Harnack inequality in the framework of harmonic spaces.

2017
27 Aprile
Francesca Colasuonno
Radial positive solutions for p-Laplacian supercritical Neumann problems

seminario di analisi matematica

In this presentation, we will analyze a p-Laplacian problem set in a ball of R^N, with homogeneous Neumann boundary conditions. The equation involves a nonlinearity g which is (p-1)-superlinear at infinity, possibly supercritical in the sense of Sobolev embeddings. The nonlinearity allows the problem to have a constant non-zero solution. In this setting, we prove via shooting method the existence, multiplicity, and oscillatory behavior (around the constant solution) of non-constant, positive, radial solutions. We show that the situation changes drastically depending on p>1. For example, in the prototype case g(s)=s^{q-1}, if p>2, the problem has infinitely many solutions for q>p. While, if p=2, the problem admits at least k non-constant solutions provided that q-2 is bigger than the (k+1)-th radial eigenvalue of the Laplacian with Neumann boundary conditions. Finally, for 1<p<2 a surprising result is found, as non-constant solutions with the same oscillatory behavior appear in couples when the radius of the domain is big enough. We will try to give a unified description and motivation for these three different situations. This is a joint work with Alberto Boscaggin (Università di Torino) and Benedetta Noris (Universitè de Picardie Jules Verne). [A. Boscaggin, F. Colasuonno, B. Noris, Multiple positive solutions for a class of p-Laplacian Neumann problems without growth conditions, preprint] [F. Colasuonno, B. Noris, A p-Laplacian supercritical Neumann problem, Discrete Contin. Dyn. Syst., Vol. 37 n. 6 (2017) 3025-3057]

2017
20 Aprile
Eleonora Cinti
Flatness results for nonlocal phase transitions in low dimensions.

seminario di analisi matematica

We present some recent results in the study of the fractional Allen-Cahn equation. In particular, we are interested in the analogue, for the fractional case, of a well known De Giorgi conjecture about one-dimensional symmetry of bounded monotone solutions. In dimension n=2 and for any fractional power 0<s<1 of the Laplacian, the conjecture is known to be true. In this seminar, we will address the 3-dimensional case. Depending wheter s is below or above 1/2, we need to exploit different techniques and ingredients in the proof of the one-dimensional symmetry. In particular, when s<1/2, some properties of the so-called nonlocal minimal surfaces, will play a crucial role. This talk is based on several papers in collaboration with X. Cabré, J. Serra, and E. Valdinoci.

2017
13 Aprile
Valentina Franceschi
The isoperimetric problem in Carnot-Carathéodory spaces

seminario di analisi matematica

The aim of this seminar is to present some results about the isoperimetric problem in Carnot-Carathéodory spaces connected with the Heisenberg geometry. The Heisenberg group is the framework of an open problem about the shape of isoperimetric sets, known as Pansu’s conjecture. We start by studying the isoperimetric problem in Grushin spaces and Heisenberg type groups, under a symmetry assumption that depends on the dimension. We emphasize a relation between the perimeter in these two types of structure. We conclude by presenting some recent results about constant mean curvature surfaces (hence about isoperimetric sets) in the Riemannian Heisenberg group, focusing our attention on the subriemannian limit.

2017
30 Marzo
Serena Federico
Local solvability of a class of degenerate second order operators

seminario di analisi matematica

In this talk we analyze the local solvability property of a class of degenerate second order partial differential operators with smooth and non-smooth coefficients. The class under consideration exhibits a degeneracy due to the interplay between the singularity associated with the characteristic set of a system of vector fields and the vanishing of a function. In particular we shall show the local solvability property of the class in the neighborhood of a set where the principal symbol of the operator can possibly change sign (which is a property that can negatively affect the local solvability of the operator).

2017
16 Marzo
Simonetta Abenda
KP theory, total positivity and rational degenerations of M-curves

seminario di analisi matematica

It is well known that real regular bounded KP (n-k,k)-line solitons are associated to soliton data in the totally non-negative part of the Grassmannian Gr(k,n) and that, in principle, they may be obtained in a certain limit from regular real quasi--periodic KP solutions. The latter class of KP solutions correspond to algebraic geometric data a la Krichever on regular M-curves according to a theorem by Dubrovin-Natanzon. In this talk I shall present some new results recently obtained in collaboration with P.G. Grinevich (LITP-RAS and Moscow State University). The purpose of our research is the connection of such two areas of mathematics using the real finite gap theory of the KP equation. I shall explain how we associate to any KP soliton data in the real totally nonnegative part of Gr(k,n) the rational degeneration of an M-curve of genus g=k(n-k) and the effective KP divisor.

2017
02 Marzo
Ermanno Lanconelli (Alma Mater Studiorum Università di Bologna)
An Inverse Problem in Potential Theory for Picone Elliptic-Parabolic PDEs.

seminario di analisi matematica

Let $\Omega$ be a domain in ${\mathbb{R}^N$. A density with the mean value property for non-negative harmonic functions in $\Omega$ is a positive l.s.c. function $w$ such that, for a suitable $ x_0 \in \Omega $, $$ u(x0) = \frac{1}{w(Ω)} \nt_{\Omega} u(y)w(y)dy $$ for every non-negative harmonic function $u$ in $\Omega$. In this case we say that $(\Omega,w,x_0)$ is a $\Delta$-triple. Existence of $\Delta$-triples on every sufficently smooth domain has been proved in 1994-1995, by Hansen and Netuka, and by Aikawa. Very recently, we have given positive answers to the following inverse problem: “Let $ (\Omega,w,x_0)$ and $(D,w',x_0)$ be $\Delta$-triples such that $\frac{w }{w(\Omega)= \frac {w'}{w'(D)} in $D ∩Ω$. Then is it true that $ \Omega = D$?” Our result contains, as particular cases, several classical potential theoretical characterizations of the Euclidean balls. Densities with the mean value property for solutions to wide classes of Picone’s elliptic-parabolic PDEs have appeared in literature since the 1954 pioneering work by B.Pini on the mean value property for caloric functions. In this talk we present an abstract inverse problem Theorem allowing to extend the previously recalled result on the $ \Delta$-triples to elliptic, parabolic and sub-elliptic PDEs. The results have been obtained in collaboration with Giovanni Cupini (Universita' di Bologna).

2017
23 Febbraio
Angelo Favini
Direct and Inverse Problems for Degenerate Differential Equations

seminario di analisi matematica

We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on (−∞;∞). Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too. Keywords: Inverse problem; First-Order problem, Second-Order problem, c0−semigroup, Periodic Solution. Joint work with: Mohammed AL Horani; Mauro Fabrizio; Hiroki Tanabe

2017
16 Febbraio
Giulio Tralli
Characterizing spheres in C^2 by their Levi curvature: a result à la Jellett

seminario di analisi matematica

In this talk we discuss a rigidity result for a class of real hypersurfaces in C^2 with constant Levi curvature. Following old techniques due to Jellett, we consider the boundaries of starshaped domains which satisfy a suitable condition. We provide as application an Aleksandrov-type result for domains with circular symmetries. This is a joint work with V. Martino.

2017
09 Febbraio
Nicola Fusco (Università di Napoli, Federico II)
Un risultato di stabilità asintotica per il flusso non locale di Mullins-Sekerka e per quello di Hele-Shaw

seminario di analisi matematica

Nel seminario presenteremo un risultato di minimalità locale per un’energia ottenuta come limite del modello di Ohta-Kawasaki. Utilizzando tale risultato mostreremo che le configurazioni tridimensionali periodiche, strettamente stabili per il funzionale dell’area, sono esponenzialmente stabili sia per il flusso non locale di Mullins-Sekerka che per quello di Hele-Shaw.

2017
26 Gennaio
Francesco di Plinio
Sparse domination of singular integral operators.

seminario di analisi matematica

Singular integral operators, which are a priori signed and non-local, can be dominated in norm, pointwise, or dually, by sparse averaging operators, which are in contrast positive and localized. The most striking consequence is that weighted norm inequalities for the singular integral follow from the corresponding, rather immediate estimates for the averaging operators. In this talk, we present several positive sparse domination results of singular integrals falling beyond the scope of classical Calderón-Zygmund theory; notably, modulation invariant multilinear singular integrals including the bilinear Hilbert transforms, variation norm Carleson operators, matrix-valued kernels, rough homogeneous singular integrals and critical Bochner-Riesz means. Joint work with Amalia Culiuc and Yumeng Ou and partly with Jose Manuel Conde-Alonso, Yen Do and Gennady Uraltsev.

2016
15 Dicembre
Alessio Martini
Sub-Elliptic Operators and sharp Multiplier Theorems

seminario di analisi matematica

Abstract. Let L be the Laplacian on R^n . The investigation of necessary and sufficient conditions for an operator of the form F (L) to be bounded on L^p in terms of smoothness properties of the spectral multiplier F is a classical and very active research area of harmonic analysis, with long-standing open problems (e.g., the Bochner–Riesz conjecture) and connections with the regularity theory of PDEs. In settings other than the Euclidean, particularly in the presence of a sub- Riemannian geometric structure, the natural substitute L for the Laplacian need not be an elliptic operator, and it may be just sub-elliptic. In this context, even the simplest questions related to the L^p -boundedness of operators of the form F (L) are far from being completely understood. I will survey recent results dealing with the case of sub-Laplacians on 2-step Carnot groups, complex and quaternionic spheres, and Grushin operators.

2016
01 Dicembre
Francesca Da Lio
α-Harmonicity in Sub-Riemannian Geometry.

seminario di analisi matematica

In this talk we will present an overview of some recent results on α-harmonic maps which are horizontal with respect to a given plane distribution.

2016
10 Novembre
Anna Miriam Benini
A landing theorem for hairs and dreadlocks of entire functions with bounded post-singular sets

seminario di analisi matematica

The Douady-Hubbard landing theorem for periodic external rays is one of the cornerstones of the successful study of polynomial dynamics. It states that, for a complex polynomial $f$ with bounded postcritical set, every periodic external ray lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic point is the landing point of at least one periodic external ray. We prove an analogue of the theorem for entire functions with bounded postsingular set. If such $f$ additionally has finite order of growth, then our result states precisely that every periodic hair of $f$ lands at a repelling or parabolic point, and again conversely every repelling or parabolic point is the landing point of at least one periodic hair. (Here a \emph{periodic hair} is a curve consisting of escaping points of $f$ that is invariant under an iterate of $f$.) For general $f$ with bounded postsingular set, but not necessarily of finite order, the role of hairs is taken by more general connected sets of escaping points, which we call \emph{dreadlocks}. This is joint work with Lasse Rempe-Gillen.

2016
16 Giugno
Michela Eleuteri
Regularity results for elliptic equations and systems with variable growth exponent

seminario di analisi matematica

We present a review on some regularity results I obtained in the last 10 years for elliptic equations whose prototype is the p(x)-Laplacian; they can be interpreted as the Euler-Lagrange equations of integral functionals appearing in the mathematical modelling of strongly anisotropic materials. Under suitable continuity assumptions on the function p, the results I'm going to present include: - Hoelder continuity results in the scalar case (also for the obstacle problem) - Calderon-Zygmund estimates for a class of obstacle problem with variable growth exponent - global regularity and stability of solutions to elliptic equations with non-standard growth - Lipschitz estimates for systems (thus in the vectorial setting) with ellipticity conditions at infinity

2016
19 Maggio
Valentina Casarino
Autofunzioni di laplaciani e sublaplaciani su sfere

seminario di analisi matematica

In questa conferenza presenteremo alcune stime L^p-L^2, per valori di p compresi fra 1 e 2, per i proiettori spettrali congiunti associati all’operatore di Laplace--Beltrami e a un sublaplaciano definito su sfere complesse e quaternioniche. Discuteremo, in particolare, il ruolo giocato dalle stime ottimali per le autofunzioni congiunte e illustreremo alcuni problemi connessi all’alta concentrazione delle armoniche sferiche.

2016
12 Maggio
Paolo Salani (Univ.Firenze)
CHARACTERIZATION OF BALLS THROUGH CONCAVITY PROPERTIES OF SOLUTIONS TO ELLIPTIC EQUATIONS

seminario di analisi matematica

I will present two (unconventional) overdetermined problems. Let $n\geq 3$ and $\Omega$ be a bounded domain in $R^n$. First: if the Newtonian potential $u$ of $\Omega$ has two homothetic convex level sets, then $\Omega$ is a ball. Second: if the Newtonian potential $u$ of $\Omega$ is $\frac{1}{2-n}$-concave (i.e. $u^{(1/(2−n)}$ is convex), then Ω is a ball. The result can be extend to the $p$-capacity potential for $p\in(1,n)$.

2016
05 Maggio
Antonia Passarelli di Napoli, Università Federico II - Napoli
Differenziabiità frazionaria per soluzioni di equazioni ellittiche non lineari

seminario di analisi matematica

Presenterò alcuni risultati di maggiore differenziabilità frazionaria per soluzioni di equazioni ellittiche non lineari in forma di divergenza del tipo divA(x;Du) = divG; contenuti in [1]. L’operatore A(x;z) ha crescita quadratica rispetto alla variabile z e la mappa parziale A(.; z) appartiene ad una opportuna classe di Besov. Proviamo che le proprietà di differenziabilità frazionaria di G si trasferiscono al gradiente della soluzione senza perdita nell’ordine di differenziazione. References [1] A. Baison, A. Clop, R. Giova, J.Orobitg, A. Passarelli di Napoli. Fractional differentiability for solutions of non linear elliptic equations - arxiv Preprint 2016.

2016
28 Aprile
Marco Mughetti
Ipoellitticità analitica di una somma di quadrati e Congettura di Treves

seminario di analisi matematica

Mentre è ben nota la caratterizzazione geometrica dell'ipoellitticità C^\infty di una somma Q di quadrati di campi vettoriali, per l'ipoellitticità analitica la questione è largamente aperta. A questo riguardo, F. Treves [1996] ha formulato una congettura secondo cui l'ipoellitticità analitica dipenderebbe dalla "regolarità" simplettica di un'opportuna stratificazione dell'insieme caratteristico di Q. In questo seminario, si discuterà un risultato, ottenuto in collaborazione con P. Albano e A. Bove, che mostra come la suddetta stratificazione non sia in realtà sufficiente a garantire l'ipoellitticità analitica di Q.

2016
21 Aprile
Tommaso Leonori (Universidad de Granada, Spagna)
Alcuni risultati di esistenza per equazioni ellittiche quasilineari

seminario di analisi matematica

 

2016
14 Aprile
Francesco Serra Cassano (Università di Trento)
Superfici minime non parametriche nel gruppo di Heisenberg

seminario di analisi matematica

Saranno presentati alcuni risultati di esistenza, unicità e regolarità per $t$- grafici e grafici intrinseci nel gruppo di Heisenberg. Inoltre saranno discussi alcuni problemi aperti in questo ambito, con particolare riguardo al problema di Bernstein.

2016
07 Aprile
Eugenio Vecchi
Steiner formula in the Heisenberg group

seminario di analisi matematica


2016
31 Marzo
Alessia Kogoj
Boundary value problem for hypoelliptic evolution equations: Perron-Wiener solution and a cone-type criterion

seminario di analisi matematica

We show how to apply Harmonic Spaces Potential Theory in studying Dirichlet problem for a general class of evolution hypoelliptic PDEs of second order. We construct Perron-Wiener solution and we show a new regularity criterion for the boundary points. Our criterion extends and generalizes the classical parabolic-cone criterion for the Heat equation due to Effros and Kazdan. The class of operator to which our results apply contains the Heat operators on stratified Lie groups and the prototypes of the Kolmogorov operators.

2016
17 Marzo
Raffaella Servadei
Nonlocal fractional problems via variational methods

seminario di analisi matematica


2016
03 Marzo
Daniele Morbidelli
Alcune questioni di regolarità per distanze subRiemanniane

seminario di analisi matematica


2016
03 Marzo
Daniele Morbidelli
Alcune questioni di regolarità per distanze subRiemanniane

seminario di analisi matematica


2016
25 Febbraio
Sergio Polidoro
Teoremi di tipo Liouville per operatori di evoluzione ipoellittici

seminario di analisi matematica

 

2015
17 Dicembre
Andrea Pinamonti
A measure zero universal differentiability set in the Heisenberg group

seminario di analisi matematica

In this talk I'll show that the Heisenberg group contains a measure zero set $N$ such that every Lipschitz function $f: H^n\to R$ is Pansu differentiable at a point of $N$. This is a joint work with G. Speight (University of Cincinnati).

2015
17 Dicembre
Davide Barbieri (Università Autonoma di Madrid)
Noncommutative Fourier analysis on invariant subspaces: frames of unitary orbits and Hilbert modules over group von Neumann algebras

seminario di analisi matematica

We give an survey of some recent results concerning the structure of bases and frames generated by unitary group orbits in Hilbert spaces. Invariant subspaces can be characterized, by means of Fourier intertwining operators, as modules whose rings of coefficients are given by group von Neumann algebras. It can be shown that these modules are naturally endowed with an unbounded operator-valued pairing which defines a noncommutative Hilbert structure. Roughly speaking, each orbit defines a point in such a Hilbert module, and the noncommutative pairing defines the analogous of a scalar product. Frames and bases obtained by countable families of orbits can then be characterized in terms of new notions of noncommutative reproducing systems, for which a full theory of linear expansions has been developed. Motivations for this study come from problems in approximation theory, concerning group generalizations of wavelets and multiresolution analysis, and issues of regular sampling in shift-invariant spaces such as generalized Paley Wiener spaces.

2015
10 Dicembre
Ermanno Lanconelli
On a direct and inverse problem in Potential Theory

seminario di analisi matematica

The Newtonian potential of a homogeneous body D is proportional, outside D, to the Newtonian potential of a mass concentrated at a point x_0 in D if and only if D is a Euclidean ball centered at x_0. The if part simply follows from Gauss Mean Value Theorem for harmonic functions. The only if part is a Theorem by Aharonov, Schiffer and Zalcman. Aim of this talk is to present an extension of the previous result to non-homogeneous bodies, obtained in collaboration with Giovanni Cupini.

2015
26 Novembre
Marco Falconi
Semiclassical analysis in infinite dimensions: Wigner measures

seminario di analisi matematica

In this talk, we review semiclassical analysis for systems whose phase space is of arbitrary (possibly infinite) dimension. An emphasis will be put on a general derivation of the so-called Wigner classical measures as the limit of states in a non-commutative algebra of quantum observables. In the remaining time, the related problem of quantization will be introduced; and we will follow the projective approach of Ammari and Nier.

2015
19 Novembre
Gregorio Chinni
The Green Operator of a Globally Analytic Hypo-elliptic Operator on the Torus and Applications

seminario di analisi matematica

(joint work with Paulo D.~Cordaro) We study the properties of the Green operator for an analytic linear PDO such that both it and its formal adjoint are globally sub-elliptic and globally analytic-hypoelliptic (GAH) in the torus. We introduce the class of M\'etivier operators, $ \mathscr{M}_{\varepsilon}(\mathbb{T}^{N})$, study the properties of its perturbations and of its analytic vectors and show that when the Green operator of $ P(x,D)$ belongs to a well defined class of analytic pseudodifferential operators on the torus then $ P(x,D) \in \mathscr{M}_{\varepsilon}(\mathbb{T}^{N})$. We present some examples of linear PDO in such class.\\ We also study (joint work with N. ~Braun Rodrigues, Paulo D.~Cordaro and M.~R.~Jahnke) the perturbation problem and the Gevrey regularity of the Gevrey vectors for a class of globally analytic hypoelliptic H\"ormander's operators defined on the $N$-dimensional torus introduced by P.~D.~ Cordaro and A.~A.Himonas.

2015
12 Novembre
Angelo Favini
Identification for general degenerate problems of hyperbolic type

seminario di analisi matematica


2015
29 Ottobre
Beatrice Abbondanza
Soluzione di Perron - Wiener e soluzione variazionale del problema di Dirichlet per una classe di operatori del secondo ordine

seminario di analisi matematica


2015
15 Ottobre
Marco Squassina
The Brezis-Nirenberg problem for the fractional p-Laplacian

seminario di analisi matematica

We overview some recent results involving the fractional p-Laplacian operator and discuss the solvability of a related Brezis-Nirenberg problem.

2015
18 Giugno
Bruno Franchi
Alzheimer’s disease: a mathematical model for onset and progression

seminario di analisi matematica


2015
15 Giugno
Francesco Fanelli (Centro di Ricerca Matematica "Ennio De Giorgi", Scuola Normale Superiore)
Viscous capillary fluids in fast rotation

seminario di analisi matematica

 
In the present talk we are interested in a singular limit problem for a compressible Navier-Stokes-Korteweg system under the action of strong Coriolis force. This is a model for compressible viscous capillary fluids, when the rotation of the Earth is taken into account. Supposing both the Mach and Rossby numbers to be proportional to a small parameter $\veps$, we are interested in the asymptotic behavior of a family of weak solutions to our model, for $\veps$ going to $0$. We consider this problem in the regimes of both constant and vanishing capillarity: we prove the convergence of the model to $2$-D Quasi-Geostrophic type equations for the limit density function. The case of variations of the rotation axis will be discussed as well.

2015
04 Giugno
Giulio Tralli
Some Zaremba-Hopf-Oleinik boundary comparison principles at characteristic points.

seminario di analisi matematica

In this talk I will discuss the validity of the Hopf lemma for certain degenerate-elliptic equations at characteristic boundary points. In the literature there are some positive results under the assumption that the boundary of the domain reflects the underlying geometry of the specific operator. I will mainly focus on conditions on the boundary which are suitable for some families of degenerate operators, also in presence of first order terms. This is a joint work with Vittorio Martino.

2015
21 Maggio
V. Georgiev
Cubic Schrodinger equation in 1-D without zero resonance and dispersive properties of its solutions

seminario di analisi matematica

We consider 1-D Schrodinger equation with cubic nonlinearity and Hamiltonian with short range potential without zero resonances. We prove existence and scattering of small data solutions.

2015
14 Maggio
Stefanie Sonner (Felix-Klein-Zentrum für Mathematik, Technische Universität Kaiserslautern)
Global attractors for semilinear parabolic problems involving $X$-elliptic operators

seminario di analisi matematica

 
We consider semilinear parabolic equations involving an operator that is $X$-elliptic with respect to a family of vector fields $X$ with suitable properties. The vector fields determine the natural functional setting associated to the problem and the admissible growth of the non-linearity. We prove the global existence of solutions and characterize their longtime behavior. In particular, we show the existence and finite fractal dimension of the global attractor of the generated semigroup and the convergence of solutions to an equilibrium solution when time tends to infinity. These results were obtained in collaboration with Alessia E. Kogoj.

2015
23 Aprile
Simonetta Abenda
Degenerazioni razionali di M-curve e grassmanniane totalmente positive

seminario di analisi matematica

In un lavoro in collaborazione con P.G. Grinevich troviamo la connessione fra la teoria delle Grassmanniane totalmente positive e le degenerazioni razionali di M-curve usando la teoria dell'equazione di Kadomtsvev-Petviashvili (KP). Ad ogni punto della grassmanniana reale totalmente positiva $GR^{TNN}_+ (N,M)$ associamo la degenrazione razionale di una M-curva di genere minimo $g=N(M-N)$ e ricostruiamo i dati algebro-geometrici alla Krichever per la corrispondente soluzione multi-solitonica dell'equazione KP. Nel presente seminario spiego l'idea alla base di tale costruzione.

2015
16 Aprile
Elvira Mascolo (Università di Firenze)
A path along the regularity of solutions to quasilinear elliptic systems

seminario di analisi matematica

We present some recent results on the local boundedness and Lipschitz continuity of weak solutions to quasilinear systems and/or local minimizers of vector-valued integral functionals. We consider systems and functionals under non standard p-q growth conditions. Moreover, in this context, the existence of weak solutions is also examined.

2015
26 Marzo
Vira Markasheva
Decay of mass and another qualitative properties of solutions to nonlinear parabolic equations in generalized Grushin settings

seminario di analisi matematica

I would like to describe in some way an asymptitoc behaviour of solutions to Cauchy problems for degenerate parabolic equations with p-Laplacian and gradient absorption term in generalized Baouendi-Grushin type settings. Among qualitative properties under the consideration will be existence, Holder continuity and some sharp estimates of radii of the supports of the solutions and essential maximums of solutions. Also the criterion for the mass decay fenomenon will be discussed.

2015
19 Marzo
Michele Pignotti
Taylor polynomials for Kolmogorov equations and applications

seminario di analisi matematica

Starting from a Kolmogorov equations arising in finance we present a method to obtain approximate solutions of the related Cauchy problem. Error estimates for small time strongly depend on the regularity of the final datum. This is our motivation to define for an homogeneous Kolmogorov operator suitable Holder spaces of every order and prove a Taylor type formula. We also compare our definitions and results with the rich related literature.

2015
12 Marzo
Giulia Sarfatti
The quaternionic Hardy space and the geometry of the unit ball

seminario di analisi matematica

The Hardy space of slice regular functions on the quaternionic unit ball H^2(B) is a reproducing kernel Hilbert space. In this talk, after an appropriate introduction to the subject, we will see how this property can be exploited to construct a Riemannian metric on B and we will study the geometry arising from this construction. We will also see that, in contrast with the example of the Poincaré metric on the complex unit disc, no Riemannian metric on B is invariant with respect to all slice regular bijective self maps of B. The results presented are obtained in collaboration with Nicola Arcozzi.

2015
26 Febbraio
Davide Barilari (Université Paris Diderot)
Sviluppo asintotico del nucleo del calore al cut locus in geometria sub-Riemanniana

seminario di analisi matematica

In questo seminario tratteremo il problema di caratterizzare lo sviluppo asintotico per tempo piccolo del nucleo del calore p_t(x, y) associato al Laplaciano sub-Riemanniano. In particolare, dopo aver ricordato i risultati noti nel caso Riemanniano e sub-Riemanniano, esamineremo l'asintotica del nucleo del calore quando y e' nel cut locus di x (tipicamente quando la distanza sub-Riemanniana d^2(x,\cdot) non e' differenziabile in y). Mostreremo come l'asintotica di p_t(x,y) riflette la struttura delle geodetiche che collegano x con y. Questi risultati (collaborazione con U. Boscain e R. Neel) sono ottenuti estendendo all'ambito sub-Riemanniano una idea di Molchanov per il caso Riemanniano.

2015
19 Febbraio
Ermanno Lanconelli
Criteri di tipo Wiener per equazioni di evoluzione

seminario di analisi matematica

 

2015
12 Febbraio
Vittorio Martino
Group actions on the sphere and multiplicity results for the CR-Yamabe equation.

seminario di analisi matematica

We will show that the CR-Yamabe equation has several families of infinitely many changing sign solutions, each of them having different symmetries. The problem is variational but it is not Palais-Smale: using different complex group actions on the sphere, we will find many closed subspaces on which we can apply the minmax argument.

2015
04 Febbraio
Petr G. Grinevich
The scattering transform for vector fields and dispersionless integrable PDE's:the Cauchy problem for the Pavlov equation.

seminario di analisi matematica

Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the scattering and inverse scattering problem associated with integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data.

2015
29 Gennaio
Angelo Favini
Inverse Problems for Parabolic Equations from Control Problems.

seminario di analisi matematica


2014
18 Dicembre
Xue Ping Wang
Gevrey estimates for resolvent of a class of non-selfadjoint Schrödinger operators

seminario di analisi matematica

It is known that the boundary values of the resolvent of selfadjoint Schrödinger operator with a slowly decreasing potential is smooth at the threshold zero. In this talk, I shall show that in a more general setting, one has in fact some Gevrey estimates for the resolvent. As applications, we show that local energies of solutions to the associated heat equation and the Schrödinger equation decay subexponentially.

2014
04 Dicembre
Alain Grigis, Université Paris 13
Resonances for a problem of homogenization

seminario di analisi matematica

 

2014
28 Ottobre
HERMANO FRID, IMPA (Rio de Janeiro)
A NOTE ON THE STOCHASTIC WEAKLY* ALMOST PERIODIC HOMOGENIZATION OF FULLY NONLINEAR ELLIPTIC EQUATIONS

seminario di analisi matematica

 

2014
25 Settembre
Vesselin Petkov
Estimates for the resolvent and spectral gaps for non self-adjoint operators

seminario di analisi matematica

In mathematical physics and dynamical systems one encounters non self-adjoint operators with spectrum not intersecting a strip, called spectral gap. The estimates of the norm of the resolvent of P in the strip play an important role in the investigation of the local decay of the energy, the analysis of the scattering resonances and the analytic continuation of the dynamical zeta function. We will discuss results and open problems concerning the estimate of the inverse of a holomorphic function without zeros in a strip and the estimates of the cut-off resolvent of the Dirichlet Laplacian for trapping perturbations.

2014
26 Giugno
Prof.ssa Loredana Lanzani, University of Arkansas e Syracuse University
L'integrale di Cauchy in C^n

seminario di analisi matematica

 

2014
12 Giugno
Vittorio Martino
A Smale type result and application to contact homology

seminario di analisi matematica

We will show that the injection of a suitable subspace of the space of Legendrian loops into the full loop space is an S^1-equivariant homotopy equivalence. Moreover, since the smaller space is the space of variations of a given action functional, we will compute the relative Contact Homology of a family of tight contact forms on the three-dimensional torus.

2014
29 Maggio
Prof. Davide Guidetti
Problemi parabolici con condizioni al contorno dinamiche negli spazi L^p

seminario di analisi matematica

 

2014
22 Maggio
Alessia Kogoj
L^p -Liouville Theorems for Invariant Evolution Equations

seminario di analisi matematica

Some L^p-Liouville theorems for several classes of evolution equations will be presented. The involved operators are left invariant with respect to Lie group composition laws in R^{n+1}. Results for both solutions and sub-solutions will be given.

2014
15 Maggio
Eleonora Cinti
A Liouville-type Theorem for a nonlinear and nonlocal problem in the Heisenberg group.
We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant operators, which can be constructed as the Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre. The main tools in our proof are the CR inversion and the moving plane method, applied to the solution of the lifted problem in the half-space $\mathbb{H}^n\times \R^+$. This is a joint work with Jinggang Tan.

2014
14 Maggio
Prof. Zoltan Balogh, University of Bern, Switzerland
How frequently can Sobolev maps distort the Hausdorff dimension? Second Part

seminario di analisi matematica


2014
09 Maggio
Prof. Zoltan Balogh, University of Bern, Switzerland
How frequently can Sobolev maps distort the Hausdorff dimension? First part.

seminario di analisi matematica

Bi-Lipchitz maps between metric spaces do not change the Hausdorff dimension of sets, while Hölder continuous maps distort dimension in a controlled way. In this talk we will consider this type of questions for the class of Sobolev mappings in the setting of foliated metric spaces. The results come from recent joint works with R. Monti, J. Tyson, K. Wildrick.

2014
10 Aprile
David Rottensteiner, Imperial College, London UK
On the Dynin-Folland Group and its Applications to Modulation Spaces on Coadjoint Orbits

seminario di analisi matematica

We give a classification of the unitary irreducible representations (unirreps) of the Dynin-Folland Group, a.k.a. the Heisenberg Group of the Heisenberg Group, and discuss the modulation spaces induced by these unirreps on their corresponding co-adjoint orbits via the Weyl-Pedersen calculus. We compare these spaces with both the classical modulation spaces and the co-orbit modulation spaces induced by the Dynin-Folland group.

2014
03 Aprile
Prof. Sergio Polidoro
Risultati di unicità per il Problema di Cauchy relativo ad operatori ipoellittici

seminario di analisi matematica


2014
27 Marzo
Andrea Bonfiglioli
Algebre di campi vettoriali completi di Hörmander, e la costruzione di gruppi di Lie

seminario di analisi matematica


2014
13 Marzo
Prof. Massimo Cicognani
Equazioni di tipo Schr\"odinger con Hamiltoniana dipendente dal tempo.

seminario di analisi matematica

Si considera il problema di Cauchy per una equazione di tipo Schr\"odinger con una Hamiltoniana dipendente dal tempo ed un termine di convezione. Si provano condizioni necessarie e sufficienti per la buona posizione in spazi di Sobolev e di Gevrey.

2014
06 Marzo
Prof. Kevin Wildrick (Université de Fribourg), ospite di Annalisa Baldi nell’ambito di un progetto GNAMPA
Dimension distortion by Sobolev mappings on the Heisenberg group

seminario di analisi matematica

The Heisenberg group is equipped with a foliation by horizontal lines that differs substantially from the standard foliation of Euclidean space by lines. We investigate the behavior of Sobolev mappings on this foliation. It is a fundamental property of Sobolev mappings that they are absolutely continuous on almost every line; we estimate the quantity of lines whose image under a Sobolev mapping has dimension at least a fixed number d>1.

2014
13 Febbraio
Prof Yehuda Pinchover (Department of Mathematics, Technion - Israel Institute of Technology, Haifa, ISRAEL)
SOME ASPECTS OF HARDY TYPE INEQUALITIES

seminario di analisi matematica

 

2014
06 Febbraio
Prof. Angelo Favini
Un approccio generale a problemi di identificazione ed applicazioni.

seminario di analisi matematica


2013
05 Dicembre
Prof. Gerardo Mendoza (Dept. of Math., Temple University)
Topological constraints of global hypoellipiticity

seminario di analisi matematica

Let M be a closed manifold, E, F be complex vector bundles over M, and P be a pseudodifferential operator mapping smooth sections of E to smooth sections of F. I will first discuss implications on the relation between E and F when P is elliptic, then implications on the relations between these vector bundles and M when E and F are line bundles, M a surface and P a first order globally hypoelliptic differential operator of principal type. At the end of the talk I will return to ellipticity and discuss some open problems. The talk is based on joint work with H.Jacobowitz (Indiana Univ. Math J., 2002 and TAMS, 2003) and with A.P.Bergamasco and S.L.Zani (Comm. PDE, 2012).

2013
06 Giugno
Prof. Abbas Bahri (Rutgers University)
Periodic Orbits of Three Dimensional Vector-Fields

seminario di analisi matematica


2013
23 Maggio
Prof. Davide Guidetti
Ricostruzione di un nucleo di convoluzione in un problema parabolico con un termine di memoria nelle condizioni al contorno

seminario di analisi matematica


2013
16 Maggio
Prof. Francois Treves, Rutgers University
Stratificazioni intrinseche di insiemi analitici reali

seminario di algebra e geometria


2013
09 Maggio
Prof. Giovanna Citti
Soluzioni fondamentali ristrette a ipersuperfici: curvatura e stime di Schauder

seminario di analisi matematica


2013
18 Aprile
Dott.Vittorio Martino
Un risultato di esistenza per l'equazione di Yamabe CR

seminario di analisi matematica

In questo seminario proveremo l'esistenza di (infinite) soluzioni a segno non costante per l'equazione di Yamabe CR. Il problema e' variazionale, ma il funzionale associato non soddisfa le condizioni di compattezza di Palais-Smale; mediante una opportuna azione di gruppo si costruira' un sottospazio sul quale sara' comunque possibile applicare un argomento di minimax di tipo Ambrosetti-Rabinowitz. Il risultato risolve una questione rimasta aperta dopo la classificazione delle soluzioni positive fatta da Jerison-Lee negli anni '80.

2013
08 Aprile
Tudor Barbu
"PDE-based image denoising, restoration and edge enhancement techniques"

seminario di analisi matematica


2013
04 Aprile
Annalisa Baldi
Lanzani-Stein inequalities in Heisenberg groups

seminario di analisi matematica


2013
14 Marzo
Prof. Marco Bramanti (Politecnico di Milano)
Stime a priori Lp e Hölderiane per operatori non variazionali modellati su campi di Hörmander con drift

seminario di analisi matematica


2013
28 Febbraio
Prof. Bruno Franchi
Grafici nei gruppi di Carnot

seminario di analisi matematica


2013
31 Gennaio
Prof. Angelo Favini
Problemi diretti ed inversi per relazioni lineari

seminario di analisi matematica


2012
08 Novembre
Prof. Artem Kozhevnikov
Vertical curves in the Heisenberg group

seminario di analisi matematica

We investigate metric properties of level sets of horizontally differentiable maps defined on the first Heisenberg group $(\Bbb{H}^1,d_{cc})$ equipped with the standard sub-Riemannian structure. In particular, we present an exhaustive analysis in a new case of a map $F\in C^1_H(\Bbb{H}^1, \Bbb{R}^2)$ with surjective horizontal differential (an analogue of the classical implicit function theorem). Among other results, we show that a level set of such map is locally a simple curve of Hausdorff sub-Riemannian dimension 2, but, surprisingly, in general its two-dimensional Hausdorff measure can be zero or infinity. Therefore, those level sets (called \textsf{vertical curves}) can be of rough nature and not belong to the class of intrinsic regular manifolds.

2012
07 Giugno
prof.Valentino Magnani (Univ.Pisa)
Stime di regolarita` per funzioni convesse rispetto a campi di Hörmander

seminario di analisi matematica

Presenteremo due stime integrali che determinano in particolare la regolarita` lipschitziana di funzioni superiormente limitate e convesse rispetto a campi di Hörmander. Gli argomenti utilizzati si basano sia sulla geometria indotta dai campi di Hörmander, che da stime integrali per sottosoluzioni di sublaplaciani.

2012
31 Maggio
prof.Sergio Polidoro (Univ.Modena)
Disuguaglianze di Harnack per operatori di evoluzione ipoellittici: aspetti geometrici ed applicazioni

seminario di analisi matematica


2012
24 Maggio
prof.Davide Guidetti
Ricostruzione di un termine di sorgente in un problema parabolico

seminario di analisi matematica


2012
26 Aprile
prof.Nicola Arcozzi
Distance from a curve in the Heisenberg group and applications

seminario di analisi matematica


2012
29 Marzo
Giulio Tralli
Proprietà di palla doppia in gruppi di Carnot di passo due

seminario di analisi matematica


2012
15 Marzo
Matteo Focardi (Univ.Firenze)
Questioni di regolarita` per minimi locali del funzionale di Mumford-Shah in dimensione 2

seminario di analisi matematica


2012
01 Marzo
Prof. Angelo Favini
Metodi perturbativi per problemi inversi su equazioni differenziali degeneri

seminario di analisi matematica


2012
23 Febbraio
Emanuele Paolini (Univ.Firenze)
Connessioni minime: il problema classico di Steiner e sue generalizzazioni

seminario di analisi matematica


2011
22 Settembre
Prof. Vesselin Petkov, Universite' de Bordeaux I
Disappearing solutions of Maxwell's equations.

seminario di analisi matematica


2011
23 Giugno
Prof Igor Verbitsky (Missouri University, Columbia)
Linear and nonlinear elliptic equations with natural growth terms. Part I

seminario di analisi matematica


2011
16 Giugno
Prof. Igor Verbitsky (University of Missouri, Columbia)
Elliptic equations of Schrodinger type

seminario di analisi matematica


2011
09 Giugno
Prof. Fausto Ferrari
Su alcune relazioni tra operatori frazionari del laplaciano e operatori hessiani

seminario di analisi matematica


2011
26 Maggio
Prof. Davide Guidetti
Un problema di determinazione del termine di sorgente in un'equazione parabolica astratta

seminario di analisi matematica


2011
26 Maggio
Dott. Gian Paolo Leonardi
Un nuovo approccio alle disuguaglianze isoperimetriche quantitative

seminario di analisi matematica


2011
12 Maggio
Dott. Daniele Morbidelli
Famiglie s-involutive di campi vettoriali, orbite associate e distanze di controllo.

seminario di analisi matematica


2011
21 Aprile
Dott.ssa Eleonora Cinti
Interpolation inequalities in pattern formation

seminario di analisi matematica


2011
07 Aprile
Prof. Ermanno Lanconelli
Bruno Pini e la disuguaglianza di Harnack parabolica. La nascita della Teoria Parabolica del Potenziale.

seminario di analisi matematica


2011
24 Marzo
Prof. Antonio Bove
Ipoellitticità e non ipoellitticità per somme di quadrati di campi complessi.

seminario di analisi matematica


2011
03 Marzo
Prof. Sergio Polidoro
Disuguaglianze di Harnack alla frontiera per equazioni di Kolmogorov

seminario di analisi matematica


2011
17 Febbraio
Dott.ssa Annalisa Baldi
Differential forms in Carnot groups: a variational approach

seminario di analisi matematica


2011
03 Febbraio
Prof. Angelo Favini
Potenze frazionarie e teoria della interpolazione per operatori lineari multivoci ed applicazioni

seminario di analisi matematica


2010
17 Giugno
Prof. Giovanni Cupini
Prescrizione del determinante jacobiano senza ipotesi di segno

seminario di analisi matematica


2010
03 Giugno
Prof. Nicola Arcozzi
Capacità d'insiemi per alberi, grafi e spazi metrici Ahlfors-regolari

seminario di analisi matematica


2010
20 Maggio
Dott. Andrea Bonfiglioli
I Teoremi di Campbell, Baker, Hausdorff e Dynkin. Storia, prove e problemi aperti

seminario di analisi matematica


2010
06 Maggio
Dott. Paolo Albano
Regolarita' delle soluzioni di viscosita' dell'equazione iconale.

seminario di analisi matematica


2010
22 Aprile
Dott. Francesco Paolo Montefalcone
Monotonia e Disuguaglianza Isoperimetrica sulle Ipersuperfici dei gruppi di Carnot

seminario di analisi matematica

Partirò illustrando una classica disuguaglianza isoperimetrica di Michael e Simon nel caso particolare delle ipersuperfici regolari dello spazio Euclideo n-dimensionale. Questo risultato verrà poi commentato avendo come scopo l'individuazione degli ingredienti-chiave necessari alla sua generalizzazione al contesto non-Euclideo dei gruppi di Carnot. In particolare, illustrerò la cosidetta "disuguaglianza di monotonia". Quindi, dopo aver introdotto le principali notazioni concernenti i gruppi di Carnot, cercherò di illustrare una tecnica che permette di generalizzare a questo setting la disuguaglianza di monotonia, ma in una versione localizzata. Darò poi alcune applicazioni, tra le quali la più importante è una versione generale della disuguaglianza isoperimetrica di Michael e Simon valida per ipersuperfici compatte -con bordo- dei gruppi di Carnot. I risultati di questo seminario si possono trovare, tra gli altri, nel preprint "Isoperimetric, Sobolev and Poincaré inequalities on hypersurfaces in sub-Riemannian Carnot groups", reperibile sul sito Arxiv all'indirizzo: http://arxiv.org/pdf/0910.5656

2010
08 Aprile
Prof. Fausto Ferrari
Sulla simmetria delle soluzioni stabili di alcune equazioni semilineari.

seminario di analisi matematica


2010
25 Marzo
Prof. Ermanno Lanconelli
Su alcune caratterizzazioni delle funzioni subarmoniche nei gruppi di Lie stratificati.

seminario di analisi matematica


2010
11 Marzo
Prof. Davide Guidetti
Moltiplicatori di Fourier vettoriali e applicazioni

seminario di analisi matematica


2010
25 Febbraio
Prof. Sergio Polidoro
Risultati di regolarità per il problema dell'ostacolo relativo ad equazioni di Kolmogorov degeneri

seminario di analisi matematica


2010
11 Febbraio
Dott. Vittorio Martino
Una Trasformata di Legendre su un modello non standard.

seminario di analisi matematica


2010
21 Gennaio
Prof. Angelo Favini
Risultati di perturbazione per operatori lineari multivoci ed applicazioni

seminario di analisi matematica


2009
18 Giugno
Prof. Bruno Franchi
Un modello elementare di diffusione della beta-amiloide nella malattia di Alzheimer

seminario di analisi matematica


2009
04 Giugno
Dott.ssa Maria Carla Tesi
Faraday's form and Maxwell's equations in Heisenberg group

seminario di analisi matematica


2009
21 Maggio
Dott.ssa Maria Manfredini
Campi vettoriali non regolari di step 2: la Poincare' e la soluzione fondamentale dell'operatore associato.

seminario di analisi matematica


2009
07 Maggio
Prof. Davide Guidetti
Un problema inverso per un’equazione delle onde lineare astratta

seminario di analisi matematica


2009
16 Aprile
Dott.ssa Eleonora Cinti
Stime dell'energia e simmetria 1-dimensionale per equazioni frazionarie

seminario di analisi matematica


2009
02 Aprile
Prof. Alberto Parmeggiani
Ipoellitticita` con perdita di molte derivate

seminario di analisi matematica


2009
19 Marzo
Prof. Fausto Ferrari
Soluzioni stabili di equazioni semilineari e disuguaglianze di tipo Poincaré con curvature nel gruppo di Heisenberg

seminario di analisi matematica


2009
05 Marzo
Dott. Marco Mughetti
Ipoellitticità per una somma di quadrati complessi

seminario di analisi matematica


2009
12 Febbraio
Dott. Daniele Morbidelli
Campi di Hormander non regolari e distanze di controllo

seminario di analisi matematica


2009
22 Gennaio
Prof. Angelo Favini
Problemi diretti e inversi per sistemi di equazioni differenziali.

seminario di analisi matematica


2008
19 Giugno
Prof. Davide Guidetti
Sviluppo asintotico delle soluzioni di un problema inverso di tipo parabolico

seminario di analisi matematica


2008
05 Giugno
Dott. Vittorio Martino
Una proprietà della direzione caratteristica per le ipersuperfici reali in C^(N+1)

seminario di analisi matematica


2008
15 Maggio
Dott.ssa Maria Carla Tesi
Forme differenziali nei gruppi di Carnot e compattezza per compensazione (parte II)

seminario di analisi matematica


2008
08 Maggio
Prof. Bruno Franchi
Forme differenziali nei gruppi di Carnot e compattezza per compensazione (parte I)

seminario di analisi matematica


2008
24 Aprile
Dott.ssa Annalisa Baldi
Ipoellitticità per operatori differenziali a valori matriciali in gruppi di Carnot.

seminario di analisi matematica


2008
03 Aprile
Prof. Nicola Arcozzi
Lo spazio di Drury-Arveson: tra analisi complessa, teoria degli operatori e geometria subriemanniana

seminario di analisi matematica


2008
06 Marzo
Dott. Andrea Bonfiglioli
La Formula di Taylor per i Gruppi Omogenei ed Applicazioni

seminario di analisi matematica


2008
21 Febbraio
Dott.ssa Chiara Cinti
Risultati di unicita' per una classe di operatori di Kolmogorov degeneri

seminario di analisi matematica


2008
07 Febbraio
Prof. Ermanno Lanconelli
Operatori di Hormander invarianti ed equazioni di Kolmogorov-Fokker-Planck

seminario di analisi matematica


2008
24 Gennaio
Prof. Angelo Favini
Problemi di identificazione per equazioni differenziali degeneri del primo e del secondo ordine in spazi di Banach

seminario di analisi matematica


2007
19 Giugno
Dott. Daniele Morbidelli
Estensioni biolomorfe di mappe CR in una classe di domini pseudoconvessi

seminario di analisi matematica


2007
05 Giugno
Prof. Angelo Cavallucci
Regolarita' delle soluzioni per un problema di calcolo delle variazioni

seminario di analisi matematica


2007
24 Maggio
Prof.ssa Giovanna Citti
Regolarita' delle superfici minime nel gruppo di Heisenberg

seminario di analisi matematica


2007
10 Maggio
Prof. Bruno Franchi
Funzioni Lipschitziane nel gruppo di Heisenberg

seminario di analisi matematica


2007
26 Aprile
Francesco Paolo Montefalcone
Ipersuperfici e formule variazionali in gruppi sub-Riemanniani

seminario di analisi matematica


2007
11 Aprile
Prof. Alberto Parmeggiani
Sulla disuguaglianza di Fefferman-Phong per sistemi

seminario di analisi matematica


2007
22 Marzo
Prof. Davide Guidetti
Un problema inverso per un'equazione delle onde fortemente smorzata

seminario di analisi matematica


2007
01 Marzo
Andrea Pascucci
Problema con ostacolo e arresto ottimo con applicazioni in finanza

seminario di analisi matematica


2007
22 Febbraio
Prof. Ermanno Lanconelli
Stime Gaussiane e teoria del potenziale per operatori di diffusione

seminario di analisi matematica


2007
01 Febbraio
Dott.ssa Chiara Cinti
Formule di rappresentazione per le soprasoluzioni di equazioni ultraparaboliche su gruppi di Lie.

seminario di analisi matematica


2007
18 Gennaio
Prof. Angelo Favini
Un sistema di equazioni differenziali operatoriali di ordini diversi in spazi di Hilbert.

seminario di analisi matematica


2006
29 Giugno
Prof. Annamaria Montanari
Formule integrali per una classe di equazioni di curvatura ed applicazioni a problemi di simmetria

seminario di analisi matematica


2006
02 Marzo
Prof.Fausto Ferrari
Regolarità delle frontiere libere piatte in problemi a due fasi per operatori ellittici

seminario di analisi matematica


2005
22 Febbraio
dott. Ferrari (Università di Bologna)
Una versione geometrica del problema del commesso viaggiatore nel gruppo di Heisenberg

seminario di analisi matematica


2004
29 Giugno
Prof. A. Cavallucci
Esistenza di soluzioni per certi tipi di equazioni differenziali implicite

seminario di analisi matematica


2004
15 Giugno
Prof. Nicola Arcozzi
Alcune disuguaglianze che vanno nel senso sbagliato

seminario di analisi matematica


2004
04 Maggio
Prof. Angelo Favini
Un problema di trasmissione in uno strato sottile

seminario di analisi matematica


2004
09 Marzo
Dott.ssa A. Montanari
Esistenza ed unicità di grafici Lipschitziani con assegnata curvatura totale secondo Levi

seminario di analisi matematica


2004
24 Febbraio
prof.ssa G. Citti
Un teorema di Dini nel gruppo di rototraslazioni

seminario di analisi matematica


2004
09 Febbraio
Dott. Fausto Ferrari
La disuguaglianza di Alexandrov-Fenchel relativa

seminario di analisi matematica


2004
26 Gennaio
Prof. Bruno Franchi
Teorema div-rot nel gruppo di Heisenberg

seminario di analisi matematica