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arXiv · 2307.15235

The Dirichlet Problem for L\'evy-stable operators with $L^2$-data

Florian Grube·Thorben Hensiek·Waldemar Schefer
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Abstract

We prove Sobolev regularity for distributional solutions to the Dirichlet problem for generators of $2s$-stable processes and exterior data, inhomogeneity in weighted $L^2$-spaces. This class of operators includes the fractional Laplacian. For these rough exterior data the theory of weak variational solutions is not applicable. Our regularity estimate is robust in the limit $s\to 1-$ which allows us to recover the local theory.

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Florian Grube, Thorben Hensiek, Waldemar Schefer. 2023-07-27. The Dirichlet Problem for L\'evy-stable operators with $L^2$-data. https://arxiv.org/abs/2307.15235

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