4 citations · 8 across the 8 of their papers we have counts for
15 papers
Interface regularity for semilinear one-phase problems
Alessandro Audrito, Joaquim Serra
We study critical points of a one-parameter family of functionals arising in combustion models. The problems we consider converge, for infinitesimal values of the parameter, to Ber…
The singular set in the Stefan problem
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
In this paper we analyze the singular set in the Stefan problem and prove the following results: - The singular set has parabolic Hausdorff dimension at most . - The solution…
Non-symmetric stable operators: regularity theory and integration by parts
Serena Dipierro, Xavier Ros-Oton, Joaquim Serra +1
We study solutions to in , being the generator of any, possibly non-symmetric, stable Lévy process. On the one hand, we study the regularity of solu…
Sharp quantitative stability for isoperimetric inequalities with homogeneous weights
Eleonora Cinti, Federico Glaudo, Aldo Pratelli +2
We prove the sharp quantitative stability for a wide class of weighted isoperimetric inequalities. More precisely, we consider isoperimetric inequalities in convex cones with homog…
Generic regularity of free boundaries for the obstacle problem
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
The goal of this paper is to establish generic regularity of free boundaries for the obstacle problem in . By classical results of Caffarelli, the free boundary is $C^…
Stable solutions to semilinear elliptic equations are smooth up to dimension 9
Xavier Cabre, Alessio Figalli, Xavier Ros-Oton +1
In this paper we prove the following long-standing conjecture: stable solutions to semilinear elliptic equations are bounded (and thus smooth) in dimension . This result,…