Spectral stability under \(L^ p\)-perturbation of the second-order coefficients
type: Item
instance of: scholarly article
title: Spectral stability under \(L^ p\)-perturbation of the second-order coefficients
zbMATH Open document ID: 0848.35082
published in: Journal of Differential Equations
publication date: 1996-10-24T00:00:00Z
review text: Spectral stability is studied for a second order uniformly elliptic operator with real measurable coefficients, satisfying Dirichlet boundary conditions. First, stability estimates for the eigenvalues are proved for the operators with \(L^p\) coefficients. In the main theorem the author establishes the Lipschitz continuity of the resolvent in trace ideals. Such a result not only implies eigenvalue stability, it also yields stability of the spectral projections and, hence, of eigenvalues and eigenfunctions. In the last part of the paper the results are applied to the problem of heat transport affected by small impurities.
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 842907
zbMATH Keywords: spectral stability
zbMATH Keywords: Lipschitz continuity of the resolvent
zbMATH Keywords: heat transport
author: Gerassimos Barbatis
reviewed by: Pavel Burda
MaRDI profile type: Publication
full work available at URL: jdeq.1996.0011
OpenAlex ID: W2054077399
DOI: 10.1006/JDEQ.1996.0011
description: scientific article; zbMATH DE number 842907