4 papers
Solution of the Mumford-Shah conjecture
Francesco Deangelis
We prove the Mumford--Shah conjecture, formulated in 1989, by completing the classification of blow-up limits of minimizers in the plane. The remaining case concerns limits whose d…
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…
Boundary regularity for the Mumford-Shah functional with Dirichlet boundary conditions
Francesco Deangelis
In this paper we consider minimizers of the Mumford-Shah functional with Dirichlet boundary conditions. We study blow-ups at the boundary and prove an epsilon-regularity theorem.
A free boundary problem for binary fluids
Roberto Benzi, Michiel Bertsch, Francesco Deangelis
A free boundary problem for the dynamics of a glasslike binary fluid naturally leads to a singular perturbation problem for a strongly degenerate parabolic partial differential equ…