A global Lipschitz continuity result for a domain-dependent Neumann eigenvalue problem for the Laplace operator

被引：7

作者：

Lamberti, PD ^{[1
]}

Lanza de Cristoforis, M ^{[1
]}

机构：

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2005年 / 216卷 / 01期

关键词：

Neumann eigenvalues and eigenvectors; Laplace operator; domain perturbation; special nonlinear operators;

D O I：

10.1016/j.jde.2005.03.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Omega be an open connected subset of R-n of finite measure for which the Poincare-Wirtinger inequality holds. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset phi(Omega) of R-n, where phi is a locally Lipschitz continuous homeomorphism of Omega onto phi(Omega). Then, we show Lipschitz-type inequalities for the reciprocals of the eigenvalues delivered by the Rayleigh quotient. Then, we further assume that the imbedding of the Sobolev space W-1,W-2(Omega) into the space L-2(Omega) is compact, and we prove the same type of inequalities for the projections onto the eigenspaces upon variation of (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：109 / 133

页数：25