Xavier Ros-Oton

activity

20112026

most citedBoundary regularity for fully nonlinear integro-differential equations

77 citations · 318 across the 51 of their papers we have counts for

collaborators

74 papers

math.AP2026

The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and $L^{2}$ -solvability

Roberto Colombo, Xavier Fernández-Real, Xavier Ros-Oton

Given $s \in (0, 1)$ and a bounded Lipschitz domain $Ω \subset R^{n}$ , we establish a quantitative Dahlberg theory for the $s$ -harmonic measure of $Ω$ , $ω_{s}^{x}$ . In the nonloc…

math.AP2026

Boundary regularity for general elliptic operators of order $2 s$

Florian Grube, Xavier Ros-Oton

We establish optimal $C^{s}$ boundary regularity for the most general class of (linear and translation invariant) nonlocal elliptic operator of order $2 s$ . Namely, we consider Lévy o…

math.AP2026

Dimension of the singular set in the parabolic obstacle problem

Alejandro Martínez, Xavier Ros-Oton

In this paper we study the singular set in the parabolic obstacle problem for general obstacles $φ \in C^{2, 1}$ . We prove that the singular set has parabolic Hausdorff dimension at…

math.AP2026

Regularity of Lipschitz free boundaries for weak solutions of Alt-Caffarelli type problems

Joan Domingo-Pasarin, Xavier Ros-Oton

Motivated by the Serrin problem, we study weak solutions of the generalised Alt-Caffarelli problem $- Δ u = f$ in $Ω$ , $u = 0$ on $\partial Ω$ , $\partial_{ν} u = Q$ on $\partial Ω$ . Our m…

math.AP2025

The Neumann problem for the fractional Laplacian: optimal regularity via the Mellin transform

Serena Dipierro, Xavier Ros-Oton, Enrico Valdinoci +1

We establish the optimal regularity of solutions to the Neumann problem for the fractional Laplacian, $(- Δ)^{s} u = h$ in $Ω$ , with the external condition $N^{s} u = 0$ in $Ω^{c}$ .…

math.AP2025

Higher regularity in nonlocal free boundary problems

Begoña Barrios, Xavier Ros-Oton, Marvin Weidner

We study the higher regularity in nonlocal free boundary problems posed for general integro-differential operators of order $2 s$ . Our main result is for the nonlocal one-phase (Ber…

The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and L2-solvability

Boundary regularity for general elliptic operators of order 2s

Dimension of the singular set in the parabolic obstacle problem

Regularity of Lipschitz free boundaries for weak solutions of Alt-Caffarelli type problems

The Neumann problem for the fractional Laplacian: optimal regularity via the Mellin transform

Higher regularity in nonlocal free boundary problems

The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and $L^{2}$ -solvability

Boundary regularity for general elliptic operators of order $2 s$