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Title: The Dirichlet problem for nonlocal elliptic operators with $C^\alpha$ exterior data
Author: Audrito, Alessandro
Ros, Xavier
Keywords: Equacions en derivades parcials
Operadors integrals
Partial differential equations
Integral operators
Issue Date: 1-Sep-2020
Publisher: American Mathematical Society (AMS)
Abstract: In this note we study the boundary regularity of solutions to nonlocal Dirichlet problems of the form $L u=0$ in $\Omega$, $u=g$ in $\mathbb{R}^{N} \backslash \Omega$, in non-smooth domains $\Omega$. When $g$ is smooth enough, then it is easy to transform this problem into an homogeneous Dirichlet problem with a bounded right-hand side for which the boundary regularity is well understood. Here, we study the case in which $g \in C^{0, \alpha}$, and establish the optimal Hölder regularity of $u$ up to the boundary. Our results extend previous results of Grubb for $C^{\infty}$ domains $\Omega$.
Note: Versió postprint del document publicat a:
It is part of: Proceedings of the American Mathematical Society, 2020, vol. 148, p. 4455-4470
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ISSN: 0002-9939
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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