The Wiener criterion for nonlocal Dirichlet problems

Abstract

We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability $s\in (0,1)$ and summability $p>1$. We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in terms of the nonlocal nonlinear potential theory.

39 pages

References in corpus (2)

• Nonlocal equations with measure data
• Regularity estimates for fractional orthotropic $p$-Laplacians of mixed order

Cited by in corpus (3)

• Wolff potential estimates and Wiener criterion for nonlocal equations with Orlicz growth
• Sharp Besov capacity estimates for annuli in metric spaces with doubling measures
• Boundary estimates and a Wiener criterion for the fractional Laplacian