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Boundary regularity and Hopf lemma for nondegenerate stable operators
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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.
Forward citations
Cited by 2 Pith papers
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Capacitary estimates for solutions to nonlocal Dirichlet problems
For nonlocal p-Laplace type equations with measurable coefficients, boundary Hölder regularity holds exactly when the exterior capacity density condition holds, with a quantitative modulus estimate.
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Boundary regularity for nonlocal elliptic equations over Reifenberg flat domains
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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