6 papers · 1 filter
Lipschitz regularity for almost minimizers of a one-phase -Bernoulli-type functional in Carnot Groups of step two
Fausto Ferrari, Enzo Maria Merlino
In this paper, in a Carnot group of step and homogeneous dimension , we prove that almost minimizers of the (horizontal) one-phase -Bernoulli-type functional…
Some counterexamples to Alt-Caffarelli-Friedman monotonicity formulas in Carnot groups
Fausto Ferrari, Davide Giovagnoli
In this paper we continue the analysis of an Alt-Caffarelli-Friedman (ACF) monotonicity formula in Carnot groups of step confirming the existence of counterexamples to the m…
Alt-Caffarelli-Friedman monotonicity formula and mean value properties in Carnot groups with applications
Fausto Ferrari, Nicolò Forcillo
In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value o…
Regularity of Lipschitz free boundaries for a -Laplacian problem with right hand side
Fausto Ferrari, Claudia Lederman
We continue our study in \cite{FL} on viscosity solutions to a one-phase free boundary problem for the -Laplacian with non-zero right hand side. We first prove that viscosity…
Some evaluations of the fractional -Laplace operator on radial functions
F. Colasuonno, F. Ferrari, P. Gervasio +1
We face a rigidity problem for the fractional -Laplace operator to extend to this new framework some tools useful for the linear case. It is known that a…
Perron's solutions for two-phase free boundary problems with distributed sources
Daniela De Silva, Fausto Ferrari, Sandro Salsa
We use Perron method to construct a weak solution to a two-phase free boundary problem with right-hand-side. We thus extend the results of the pioneer work of Caffarelli for the ho…