Burenkov, Victor and Feleqi, Ermal ![]() |
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 |
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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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