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

  • Gianni Dal Maso (a1) and Annalisa Malusa (a1)


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.



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

  • Gianni Dal Maso (a1) and Annalisa Malusa (a1)


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