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arXiv · 2203.16815

The Wiener criterion for nonlocal Dirichlet problems

Minhyun Kim·Ki-Ahm Lee·Se-Chan Lee
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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.

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Minhyun Kim, Ki-Ahm Lee, Se-Chan Lee. 2022-03-31. The Wiener criterion for nonlocal Dirichlet problems. https://doi.org/10.1007/s00220-023-04632-w

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