Spectral stability estimates for the eigenfunctions of second order elliptic operators

Burenkov, Victor and Feleqi, Ermal ORCID: https://orcid.org/0000-0002-9661-0684 2012. Spectral stability estimates for the eigenfunctions of second order elliptic operators. Mathematische Nachrichten 285 (11-12) , pp. 1357-1369. 10.1002/mana.201100250

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Abstract

Stability of the eigenfunctions of nonnegative selfadjoint second-order linear elliptic operators subject to homogeneous Dirichlet boundary data under domain perturbation is investigated. Let Ω, equation image be bounded open sets. The main result gives estimates for the variation of the eigenfunctions under perturbations Ω′ of Ω such that equation image in terms of powers of ε, where the parameter ε > 0 is sufficiently small. The estimates obtained here hold under some regularity assumptions on Ω, Ω′. They are obtained by using the notion of a gap between linear operators, which has been recently extended by the authors to differential operators defined on different open sets.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Elliptic operators; Dirichlet boundary conditions; stability estimates for the eigenfunctions; perturbation of an open set; gap between linear operators; msc (2010) 47F05; 35J40; 35B30; 35P15
Publisher:	Wiley-Blackwell
ISSN:	0025-584X
Date of Acceptance:	5 December 2011
Last Modified:	31 Oct 2022 10:26
URI:	https://orca.cardiff.ac.uk/id/eprint/84897

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