Domain Perturbation for Elliptic Equations Subject to Robin Boundary Conditions

We prove domain perturbation theorems for linear and nonlinear elliptic equations under Robin boundary conditions. The theory allows very singular perturbation of domains. In particular, it includes cutting holes, parts degenerating to a set of measure zero such as the dumbbell problem, or wildly os...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 138; no. 1; pp. 86 - 132
Main Authors Dancer, E.N., Daners, D.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 20.07.1997
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ISSN0022-0396
1090-2732
DOI10.1006/jdeq.1997.3256

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Summary:We prove domain perturbation theorems for linear and nonlinear elliptic equations under Robin boundary conditions. The theory allows very singular perturbation of domains. In particular, it includes cutting holes, parts degenerating to a set of measure zero such as the dumbbell problem, or wildly oscillating boundaries. In the last case we show that the limiting problem is the Dirichlet problem.
ISSN:0022-0396
1090-2732
DOI:10.1006/jdeq.1997.3256