Spectral stability estimates for the eigenfunctions of second order elliptic operators
type: Item
instance of: scholarly article
title: Spectral stability estimates for the eigenfunctions of second order elliptic operators
zbMATH Open document ID: 1268.47054
author: Ermal Feleqi
author: Victor I. Burenkov
published in: Mathematische Nachrichten
publication date: 2012-09-06T00:00:00Z
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35P15
zbMATH DE Number: 6078246
zbMATH Keywords: elliptic operators
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: stability estimates for the eigenfunctions
zbMATH Keywords: perturbation of an open set
zbMATH Keywords: gap between linear operators
MaRDI profile type: Publication
full work available at URL: mana.201100250
OpenAlex ID: W2155407318
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DOI: 10.1002/MANA.201100250
review text: The paper deals with stability of the eigenfunctions of nonnegative selfadjoint second-order linear elliptic operators subject to homogeneous Dirichlet boundary data under domain perturbation. Precisely, let \(\Omega,\Omega'\subset\mathbb R^n\) be bounded and open sets. The main result of the paper provides estimates for the variation of the eigenfunctions under perturbations \(\Omega'\) of \(\Omega\) such that NEWLINE\[NEWLINE \Omega_\varepsilon=\left\{x\in\Omega:\operatorname{dist}(x,\mathbb R^n\setminus\Omega)>\varepsilon\right\}\subset\Omega'\subset\overline{\Omega'} \subset\Omega NEWLINE\]NEWLINE in terms of powers of the small enough parameter \(\varepsilon>0\). These estimates hold under suitable regularity assumptions on \(\Omega\) and \(\Omega'\), and are obtained by means of the notion of gap between linear operators, which has been recently extended by the authors to differential operators defined on different open sets [\textit{V. I. Burenkov} and \textit{E. Feleqi}, Math. Nachr. 286, No.~5--6, 518--535 (2013; Zbl 1268.47055)].
reviewed by: Dian K. Palagachev
description: scientific article; zbMATH DE number 6078246