Estimates for the deviation of solutions and eigenfunctions of second-order elliptic Dirichlet boundary value problems under domain perturbation
type: Item
instance of: scholarly article
title: Estimates for the deviation of solutions and eigenfunctions of second-order elliptic Dirichlet boundary value problems under domain perturbation
zbMATH Open document ID: 1334.35185
author: Ermal Feleqi
published in: Journal of Differential Equations
publication date: 2015-12-18T00:00:00Z
review text: The paper under review deals with second-order uniformly elliptic operators of the form \[ Su=-\operatorname{div} (A(x)Du)+b(x)u\quad \text{in}\;\mathbb{R}^N \] with locally \(C^{1,\alpha}\) coefficients, \(\alpha\in(0,1].\) Estimates in suitable Lebesgue or Sobolev spaces are derived for the deviation of solutions and eigenfunctions of the Dirichlet problem for \(S\) subject to domain perturbation, in terms of the natural distances between the domains. The main estimates are formulated via certain natural and easily computable ``atlas'' distances for domains with Lipschitz continuous boundaries. As a corollary, similar estimates in terms of more ``classical'' distances, such as the Hausdorff distance or the Lebesgue measure of the symmetric difference of domains, are derived. Sharper estimates are also proved to hold in smoother classes of domains.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 6522103
zbMATH Keywords: boundary value problems
zbMATH Keywords: domain perturbation
zbMATH Keywords: eigenfunctions
zbMATH Keywords: stability estimates
MaRDI profile type: Publication
full work available at URL: j.jde.2015.10.038
OpenAlex ID: W2215931383
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DOI: 10.1016/J.JDE.2015.10.038
description: scientific article; zbMATH DE number 6522103