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The Wiener criterion for nonlocal Dirichlet problems

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arxiv 2203.16815 v1 pith:HVN3VZDJ submitted 2022-03-31 math.AP

Minhyun Kim , Ki-Ahm Lee , Se-Chan Lee This is my paper · ORCID
classification math.AP
keywords nonlocalboundarycriteriondirichletproblemswienerbehaviorcharacterizes
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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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  1. An Inverse Obstacle Problem for the Fractional Schr\"odinger Equation

    math.AP 2026-07 accept novelty 6.0 of 10

    A countable family of scaled exterior measurements of the fractional Schrödinger obstacle problem determines the nonnegative potential throughout the domain.

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