On the Wiener criterion in higher dimensions

Boundary value problems

Tariq Ismaeel¹ 

[1] School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China

关键词: Wiener criterion;    Laplace equation;    Dirichlet problem;    boundary regularity;    35A01;    35B65;    35J05;    35J25;   

DOI  :  10.1186/s13661-017-0907-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The Wiener criterion is a sufficient and necessary condition for the solvability of the Dirichlet problem. However, its geometric interpretation is not clear. In the case that the domain satisfies an exterior spine condition, the requirement for the spine is clear in dimension 3. In this note, we intend to obtain the condition that the exterior spine should satisfy in higher dimensions.

【 授权许可】

CC BY