Spectral stability of the Neumann Laplacian

被引：45

作者：

Burenkov, VI

Davies, EB

机构：

[1] Cardiff Univ, Sch Math, Cardiff CF24 4YH, S Glam, Wales

[2] Kings Coll London, Dept Math, London WC2R 2LS, England

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2002年 / 186卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Neumann Laplacian; Sobolev inequalities; Hardy inequalities; spectral stability; Holder continuity;

D O I：

10.1016/S0022-0396(02)00033-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the equivalence of Hardy- and Sobolev-type inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space, We also prove that if one perturbs the boundary of the region within a uniform Holder category, then the eigenvalues of the Neumann Laplacian change by a small and explicitly estimated amount. (C) 2002 Elsevier Science (USA). All rights reserved.

引用

页码：485 / 508

页数：24

共 14 条

[1]

[Anonymous], 1989, CAMBRIDGE TRACTS MAT

[2]

[Anonymous], SPECTRAL THEORY DIFF

[3] Some embeddings of weighted Sobolev spaces on finite measure and quasibounded domains [J].