Critical points of the symmetric functions of the eigenvalues of the Laplace operator and overdetermined problems

被引：14

作者：

Lamberti, Pier Domenico ^{[1
]}

Lanza de Cristoforis, Massimo ^{[1
]}

机构：

[1] Univ Padua, Dipartimento Matemat Pura & Applicata, I-35131 Padua, Italy

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2006年 / 58卷 / 01期

关键词：

Dirichlet and Neumann eigenvalues and eigenfunctions; Laplace operator; overdetermined problems; domain perturbation; special nonlinear operators;

D O I：

10.2969/jmsj/1145287100

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Dirichlet and the Neumann eigenvalue problem for the Laplace operator on a variable nonsmooth domain, and we prove that the elementary symmetric functions of the eigenvalues splitting from a given eigenvalue upon domain deformation have a critical point at a domain with the shape of a ball. Correspondingly, we formulate overdetermined boundary value problems of the type of the Schiffer conjecture.

引用

页码：231 / 245

页数：15

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