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Approximation of relaxed Dirichlet problems by boundary value problems in perforated domains

Published online by Cambridge University Press:  14 November 2011

Gianni Dal Maso  and
Annalisa Malusa
Gianni Dal Maso
Affiliation:
SISSA, Via Beirut 2/4, 34014 Trieste, Italy
Annalisa Malusa
Affiliation:
SISSA, Via Beirut 2/4, 34014 Trieste, Italy
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Abstract

Given an elliptic operator L on a bounded domain Ω ⊆ Rn, and a positive Radon measure μ on Ω, not charging polar sets, we discuss an explicit approximation procedure which leads to a sequence of domains Ωh ⊇ Ω with the following property: for every f ∈ H−1(Ω) the sequence uh of the solutions of the Dirichlet problems Luh = f in Ωh, uh = 0 on ∂Ωh, extended to 0 in Ω\Ωh, converges to the solution of the “relaxed Dirichlet problem” Lu + μu = f in Ω, u = 0 on ∂Ω.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 1 , 1995 , pp. 99 - 114
Copyright
Copyright © Royal Society of Edinburgh 1995

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