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

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 cer...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 260; no. 4; pp. 3448 - 3476
Main Author Feleqi, Ermal
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.02.2016
Subjects
Boundary value problems
Domain perturbation
Eigenfunctions
Solutions
Stability estimates
Boundary value problems
35J40
47B25
Solutions
35P15
Stability estimates
Eigenfunctions
47A75
Domain perturbation
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ISSN0022-0396
1090-2732
DOI10.1016/j.jde.2015.10.038

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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2015.10.038