The Neumann problem for the fractional Laplacian: regularity up to the boundary

被引：0

作者：

Audrito, Alessandro ^{[1
]}

Felipe-Navarro, Juan-Carlos ^{[2
]}

Ros-Oton, Xavier ^{[3
,4
,5
]}

机构：

[1] Dept Math DISMA, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Univ Complutense Madrid, Dept Anal Matematico & Matemat Aplicada, Pl Ciencias 2, Madrid 28040, Spain

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

[4] Univ Barcelona, Dept Matematiques & Informat, Gran Via Corts Catalanes 585, Barcelona 08007, Spain

[5] Ctr Recerca Matemat, Barcelona, Spain

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2023年 / 24卷 / 02期

基金：

瑞士国家科学基金会; 欧洲研究理事会;

关键词：

ELLIPTIC-EQUATIONS; DIRICHLET PROBLEM; MU-TRANSMISSION; DOMAINS; INEQUALITIES; THEOREM;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the regularity up to the boundary of solutions to the Neumann problem for the fractional Laplacian. We prove that if u is a weak solution of.A/su D f in and Nsu D 0 in c, then u is C. up to the boundary for some. > 0. Moreover, in case s > 1 2, we show that u 2 C2s 1C../. To prove these results we need, among other things, a delicate Moser iteration on the boundary with some logarithmic corrections. Our methods allow us to treat as well the Neumann problem for the regional fractional Laplacian, and we establish the same boundary regularity result. Prior to our results, the interior regularity for these Neumann problems was well understood, but near the boundary even the continuity of solutions was open.

引用

页码：1155 / 1222

页数：68

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