7 citations · 8 across the 6 of their papers we have counts for
10 papers · 1 filter
Integro-Differential Elliptic Equations
Xavier Fernández-Real, Xavier Ros-Oton
This book aims to provide a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. Such a class of…
regularity in semilinear free boundary problems
Daniel Restrepo, Xavier Ros-Oton
We study the higher regularity of solutions and free boundaries in the Alt-Phillips problem , with . Our main results imply that, once free boundaries are $C…
Optimal regularity for nonlocal elliptic equations and free boundary problems
Xavier Ros-Oton, Marvin Weidner
In this article we establish for the first time the boundary regularity of solutions to nonlocal elliptic equations with kernels . This was known to h…
Schauder and Cordes-Nirenberg estimates for nonlocal elliptic equations with singular kernels
Xavier Fernández-Real, Xavier Ros-Oton
We study integro-differential elliptic equations (of order ) with variable coefficients, and prove the natural and most general Schauder-type estimates that can hold in this se…
Obstacle problems for nonlocal operators with singular kernels
Xavier Ros-Oton, Marvin Weidner
In this paper we establish optimal regularity estimates and smoothness of free boundaries for nonlocal obstacle problems governed by a very general class of integro-differential op…
On the regularity of the free boundary in the -Laplacian obstacle problem
Alessio Figalli, Brian Krummel, Xavier Ros-Oton
We study the regularity of the free boundary in the obstacle for the -Laplacian, in . Here, $Δ_p u=\textrm{div}\bigl(|\na…