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https://hdl.handle.net/2445/175170
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: https://doi.org/10.1090/proc/15121 |
It is part of: | Proceedings of the American Mathematical Society, 2020, vol. 148, p. 4455-4470 |
URI: | https://hdl.handle.net/2445/175170 |
Related resource: | https://doi.org/10.1090/proc/15121 |
ISSN: | 0002-9939 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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