THE DIRICHLET PROBLEM FOR NONLOCAL ELLIPTIC OPERATORS WITH C0,α EXTERIOR DATA

被引：7

作者：

Audrito, Alessandro ^{[1
,2
]}

Ros-Oton, Xavier ^{[2
,3
,4
]}

机构：

[1] Politecn Torino, Inst Math DISMA, Corso Duca degli Abruzzi 24, I-10129 Turin, Italy

[2] Univ Zurich, Dept Math, Winterthurerstr 190, CH-8057 Zurich, Switzerland

[3] ICREA, Passeig Lluis Companys 23, Barcelona 08010, Spain

[4] Univ Barcelona, Dept Matemat & Informat, Gran Via 585, Barcelona 08007, Spain

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 148卷 / 10期

基金：

欧洲研究理事会; 瑞士国家科学基金会;

关键词：

Nonlocal equations; boundary regularity; REGULARITY THEORY; EQUATIONS;

D O I：

10.1090/proc/15121

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we study the boundary regularity of solutions to non-local Dirichlet problems of the form Lu = 0 in Omega, u = g in R-N\Omega, in non-smooth domains Q. 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 is an element of C-0,C-alpha, and establish the optimal Holder regularity of u up to the boundary. Our results extend previous results of Grubb for C-infinity domains Omega.

引用

页码：4455 / 4470

页数：16

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