# name
The Dirichlet problem for nonlocal elliptic operators with $C^\alpha$ exterior data

# metadata.dc.description.abstract[].value
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 $\Omega$.

# metadata.dc.relation.ispartof[].value
Proceedings of the American Mathematical Society, 2020, vol. 148, p. 4455-4470

# metadata.dc.rights[].value
cc-by-nc-nd (c) American Mathematical Society (AMS), 2020

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
The Dirichlet problem for nonlocal elliptic operators with $C^\alpha$ exterior data