Estimates for the deviation of solutions and eigenfunctions of second-order elliptic Dirichlet boundary value problems under domain perturbation

Feleqi, Ermal ORCID: https://orcid.org/0000-0002-9661-0684 2016. Estimates for the deviation of solutions and eigenfunctions of second-order elliptic Dirichlet boundary value problems under domain perturbation. Journal of Differential Equations 260 (4) , pp. 3448-3476. 10.1016/j.jde.2015.10.038

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Abstract

Estimates in suitable Lebesgue or Sobolev norms for the deviation of solutions and eigenfunctions of second-order uniformly elliptic Dirichlet boundary value problems subject to domain perturbation in terms of natural distances between the domains are given. 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Boundary value problems; Domain perturbation; Solutions; Eigenfunctions; Stability estimates
Publisher:	Elsevier
ISSN:	0022-0396
Date of First Compliant Deposit:	1 December 2016
Date of Acceptance:	24 August 2015
Last Modified:	02 Nov 2022 09:50
URI:	https://orca.cardiff.ac.uk/id/eprint/96523

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