5 papers
Superlinear free-discontinuity models: relaxation and phase-field approximation
Sergio Conti, Matteo Focardi, Flaviana Iurlano
In this paper we develop the Direct Method in the Calculus of Variations for free-discontinuity energies whose bulk and surface densities exhibit superlinear growth, respectively f…
Stochastic homogenization of fractional obstacle problems
Francesco Deangelis, Matteo Focardi, Caterina Ida Zeppieri
We prove a stochastic homogenization result for a class of \emph{nonlinear} and \emph{nonlocal} variational problems in domains with many small randomly distributed (bilateral) obs…
The regularity theory for the Mumford-Shah functional on the plane
Camillo De Lellis, Matteo Focardi
The aim of these notes is to give a complete self-contained account of the current state of the art in the regularity for planar minimizers and critical points of the Mumford-Shah…
The classical obstacle problem with Hölder continuous coefficients
Giovanna Andreucci, Matteo Focardi
Weiss' and Monneau's type quasi-monotonicity formulas are established for quadratic energies having matrix of coefficients which are Dini, double-Dini continuity, respectively. Fre…
On the free boundary for thin obstacle problems with Sobolev variable coefficients
Giovanna Andreucci, Matteo Focardi, Emanuele Spadaro
We establish a quasi-monotonicity formula {for an intrinsic frequency function related to solutions to} thin obstacle problems with zero obstacle driven by quadratic energies with…