An overdetermined problem for elliptic equations

被引：0
|
作者：
Kalmenov, Tynysbek [1 ]
Kakharman, Nurbek [1 ]
机构：
[1] Inst Math & Math Modeling, Pushkin Str 125, Alma Ata 050010, Kazakhstan
来源：
AIMS MATHEMATICS | 2024年 / 9卷 / 08期
关键词：
overdetermined problem; Schi ff er conjecture; Dirichlet condition; Neumann condition; Newton potential;
D O I：
10.3934/math.20241002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to finding a necessary and sufficient condition for the solvability of the overdetermined problem for Poisson's equation with both the Dirichlet and Neumann conditions on the entire boundary. The proof is based on the boundary condition formula for the Newton potential. The obtained results are also extended to general second-order linear elliptic equations. As a byproduct, we present a characterization of the Schiffer property. It gives a definitive answer to the Schiffer problem.
引用
收藏
页码：20627 / 20640
页数：14
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