Subjects of research


Fractional laplace operators.
Partial differential equations: fully nonlinear.
equations, elliptic p.d.e. on nonregular domains, subelliptic operators.
Schwarz symmetrization, variational inequalities.
Free boundary problems: regularity of the free boundary.
Isoperimetric inequalities: relative isoperimetric inequalities, curvature measures and quermassintegrals.

 

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CURRICULUM (English), for the updated list of publications see the italian curriculum

CURRICULUM (Italian)

Meetings:

INDAM SCHOOL ON SYMMETRY FOR ELLIPTIC PDEs, Roma, May 25-29, 2009

SEMINARI DI ANALISI MATEMATICA, giornata in ricordo di Bruno Pini  Bologna 27 Novembre 2009

MATHEMATICS & APPLICATIONS,  Milan, January 11, 2010 and  Cagliari, June 3-5, 2010

SEMINARI DI ANALISI MATEMATICA, giornata in ricordo di Bruno Pini  Bologna 26 Novembre 2010

SEMINARI DI ANALISI MATEMATICA, giornata in ricordo di Bruno Pini  Bologna 25 Novembre 2011

PHASE TRANSITION PROBLEMS AND NONLINEAR PDEs, School/Workshop, Bologna, March 9-11, 2015



Some recent papers:

De Silva, Daniela; Ferrari, Fausto; Salsa, Sandro Free boundary regularity for fully nonlinear non-homogeneous two-phase problems. J. Math. Pures Appl. (9) 103 (2015), no. 3, 658–694.

Ferrari, Fausto; Franchi, Bruno Harnack inequality for fractional sub-Laplacians in Carnot groups. Math. Z. 279 (2015), no. 1-2, 435–458.

Ferrari, Fausto Mean value properties of fractional second order operators. Commun. Pure Appl. Anal. 14 (2015), no. 1, 83–106.

Ferrari, Fausto; Pinamonti, Andrea Characterization by asymptotic mean formulas of q-harmonic functions in Carnot groups. Potential Anal. 42 (2015), no. 1, 203–227.

Ferrari, Fausto; Medina, Maria; Peral, Ireneo Biharmonic elliptic problems involving the 2nd Hessian operator. Calc. Var. Partial Differential Equations 51 (2014), no. 3-4, 867–886Fausto Ferrari; Verbitsky, Igor E.. Radial fractional Laplace operators and Hessian inequalities. J. Differential Equations 253 (2012), no. 1, 244–272.

Ferrari, Fausto Some a priori estimates for a class of operators in the Heisenberg group. Ann. Mat. Pura Appl. (4) 193 (2014), no. 4, 1019–1040.

De Silva, Daniela; Ferrari, Fausto; Salsa, Sandro Two-phase problems with distributed sources: regularity of the free boundary. Anal. PDE 7 (2014), no. 2, 267–310.

Ferrari, Fausto; Liu, Qing; Manfredi, Juan J. On the horizontal mean curvature flow for axisymmetric surfaces in the Heisenberg group. Commun. Contemp. Math. 16 (2014), no. 3, 1350027, 41 pp.

Ferrari, Fausto; Liu, Qing; Manfredi, Juan On the characterization of p-harmonic functions on the Heisenberg group by mean value properties. Discrete Contin. Dyn. Syst. 34 (2014), no. 7, 2779–2793.

Ferrari, Fausto; Salsa, Sandro Two-phase free boundary problems for parabolic operators: smoothness of the front. Comm. Pure Appl. Math. 67 (2014), no. 1, 1–39.

Fausto Ferrari; Franchi, Bruno; Verbitsky, Igor E.. Hessian inequalities and the fractional Laplacian. J. Reine Angew. Math. 667 (2012), 133–148

Citti, Giovanna; Fausto Ferrari. A sharp regularity result of solutions of a transmission problem. Proc. Amer. Math. Soc. 140 (2012), no. 2, 615–620.

Fausto Ferrari; Valdinoci, Enrico.  Density estimates for a fluid jet model in the Heisenberg group. J. Math. Anal. Appl. 382 (2011), no. 1, 448–468.

Fausto Ferrari. Some inequalities associated with semilinear elliptic equations with variable coefficients and applications. Symmetry for elliptic PDEs, 81–104, Contemp. Math., 528, Amer. Math. Soc., Providence, RI, 2010.

Fausto Ferrari; Sandro Salsa.  Regularity of the solutions for parabolic two-phase free boundary problems. Comm. Partial Differential Equations 35 (2010), no. 6, 1095–1129

I. Birindelli, F. Ferrari, E. Valdinoci, Semilinear PDEs
in the Heisenberg group: the role of the right invariant vector fields,  Nonlinear Analysis Series A: Theory, Methods & Applications (in corso di stampa apparirŕ nel numero 72, 987--997 (2010)); doi:10.1016/j.na.2009.07.039

Fausto Ferrari, Enrico Valdinoci,
A geometric inequality in the Heisenberg group and its applications to stable solutions of semilinear problems,
to appear in Math. Ann., avalaible on line  http://dx.doi.org/10.1007/s00208-008-0274-8

Nicola Arcozzi, Fausto Ferrari,
The Hessian of the distance from a surface in the Heisenberg group , Annales Academić Scientiarum Fennicć Mathematica, 33, 35-63 (2008).

Fausto Ferrari, Bruno Franchi, Hervé Pajot,
The Geometric Traveling Salesman Theorem in the Heisenberg group,   Revista Mathematica Iberoamericana, Volume 23, Number 2, 437-480 (2007).

Fausto Ferrari, Sandro Salsa,
Regularity of the free boundary in two-phase Problems  for linear elliptic operators, Advances in Mathematics 214, 288-322, (2007)  .

Fausto Ferrari, A Steiner formula in the Heisenberg group, (preprint 2006)

Nicola Arcozzi, Fausto Ferrari,
Metric normal and distance function in the  Heisenberg group (Received: 11 March 2005  Accepted: 9 September 2006  Published online: 6 January 2007 in Mathematische Zeitschrift), Volume 256,3,
661-684 (2007)

Fausto Ferrari,
Two-phase problems for a class of fully nonlinear elliptic operators. Lipschitz free boundaries are $C^{1,\gamma}$,   American Journal of Mathematics 128, 3, 541--571 (2006)

Fausto Ferrari, Sandro Salsa,
Subsolutions of elliptic operators in divergence form and application to two-phase free boundary problems, Bound. Value Probl. 2007, Art. ID 57049, 21 pp.

Fausto Ferrari, Bruno Franchi, Hervé Pajot,
The Geometric Traveling Salesman Theorem in the Heisenberg group, (Prépublication de L'INSTITUT FOURIER Université de Grenoble I, CNRS, n. 667, Anneé 2005), accepted paper, to appear in Revista Mathematica Iberoamericana.

Fausto Ferrari, Bruno Franchi, Guozhen Lu,
On a relative Alexandrov-Fenchel inequalitiy for convex bodies in Euclidean spaces,   Forum Mathematicum 18, 907-921 (2006)

Fausto Ferrari,
Harnack inequality for two-weight subelliptic p-Laplace operators,   Mathematische Nachrichten, Vol 279, 8,  815-830  (2006)

M. Cristina Cerutti, Fausto Ferrari, Sandro Salsa,
Two phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are C^{1,\gamma},
Archive for Rational Mechanics and Analysis, Vol 171, n.3, pp. 329 - 348 (2004)

Fausto Ferrari, Bruno Franchi,
A local doubling formula for the harmonic measure associated with subelliptic operators and applications,
Communication in Partial Differential Equations, vol 28 (1,2) 1-60 ( 2003).
 

SUBMITTED PAPERS

D. De Silva, F. Ferrari, S. Salsa, Two-phase problems with distributed source: regularity of the free
boundary, arXiv:1210.7226 (2012) submitted.

F. Ferrari, Q. Liu, J.J Manfredi, On the characterization of p−harmonic functions on the Heisenberg
group by mean value properties arXiv:1210.2881v1 (2012) submitted

F. Ferrari, Q. Liu, J.J Manfredi, On the horizontal mean curvature flow for axisymmetric surfaces in
the Heisenberg group arXiv:1210.1086v1 (2012) submitted

F. Ferrari, B. Franchi, Harnack inequality for fractional sub-Laplacians in Carnot groups
arXiv:1206.0885v3 (2012) submitted. 

F. Ferrari, A. Pinamonti, Nonexistence results for semilinear equations in Carnot groups arXiv: (2012)
submitted

F. Ferrari, Some a priori estimates for a class of operators in the Heisenberg group (2012)submitted.

F. Ferrari, S. Salsa Two-phase free boundary problems for parabolic operators: smoothness of the front,
(2011) submitted.

N. Arcozzi, F. Ferrari, F. Montefalcone, CC-distance and metric normal of smooth hypersurfaces in
sub-Riemannian, Carnot groups, arXiv:0910.5648 (2009) submitted.