Boundary regularity and Hopf lemma for nondegenerate stable operators

Florian Grube

Boundary regularity and Hopf lemma for nondegenerate stable operators

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arxiv 2410.00829 v1 pith:MYEPEEXC submitted 2024-10-01 math.AP

Florian Grube This is my paper · ORCID

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keywords boundaryregularityequationslemmaoperatorsstableadditionalbounded

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abstract

We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional Laplacian. A Hopf-type boundary lemma is proven, too. An additional feature of this work is that the regularity estimate is robust as $s\to 1-$ and we recover the classical results for second order equations.

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Boundary regularity for nonlocal elliptic equations over Reifenberg flat domains
math.AP 2025-02 conditional novelty 6.0 of 10

For operators comparable to the fractional Laplacian of order 2s, solutions with zero exterior data on Reifenberg flat domains are C^{s-ε} up to the boundary.

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