From the 1 of 13 linked papers with an AI index.
13 papers
The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and -solvability
Roberto Colombo, Xavier Fernández-Real, Xavier Ros-Oton
The paper develops a quantitative Dahlberg theory for the fractional Laplacian on bounded Lipschitz domains, proving reverse‑Hölder estimates for the s‑harmonic measure and establi…
Boundary regularity for general elliptic operators of order
Florian Grube, Xavier Ros-Oton
We establish optimal boundary regularity for the most general class of (linear and translation invariant) nonlocal elliptic operator of order . Namely, we consider Lévy…
Dimension of the singular set in the parabolic obstacle problem
Alejandro MartÃnez, Xavier Ros-Oton
In this paper we study the singular set in the parabolic obstacle problem for general obstacles . We prove that the singular set has parabolic Hausdorff dimension at…
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 in , on , on .…
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, in , with the external condition in $Ω^c…
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 . Our main result is for the nonlocal one-phase (Ber…