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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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
Some recent papers:
F. Ferrari, S.Salsa, Regularity of the solutions for parabolic
two-phase free boundary problems, accettato per la
pubblicazione, apparirà in Communications in Part. Diff.
Equations.
I. Birindelli, F. Ferrari, E. Valdinoci, Semilinear PDEs
in the Heisenberg group: the role of the right invariant vector fields,
accettato per la pubblicazione apparirà in Nonlinear Analysis
Series A: Theory, Methods & Applications (in corso di stampa
apparirà 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 Academiæ Scientiarum Fennicæ
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).
IN PREPARATION