32 citations · 98 across the 23 of their papers we have counts for
32 papers
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…
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…
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…
Approximation of functions with possibly infinite jump set
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We prove an approximation result for functions such that is -integrable, , and is integrable over the jump set…
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…
Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We consider a family of vectorial models for cohesive fracture, which may incorporate -invariance. The deformation belongs to the space of generalized functions of…