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Spectral stability of the Robin Laplacian

  • V. I. Burenkov
  • M. Lanza de Cristoforis
Article

Abstract

We consider the Robin Laplacian in two bounded regions Ω1 and Ω2 of ℝ N with Lipschitz boundaries and such that Ω2 ⊂ Ω1, and we obtain two-sided estimates for the eigenvalues λ n,2 of the Robin Laplacian in Ω2 via the eigenvalues λ n, 1 of the Robin Laplacian in Ω1. Our estimates depend on the measure of the set difference Ω\Ω2 and on suitably defined characteristics of vicinity of the boundaries Ω1 and Ω2, and of the functions defined on Ω1 and on Ω2 that enter the Robin boundary conditions.

Keywords

Sobolev Space STEKLOV Institute Neumann Problem Lipschitz Continuity Lipschitz Boundary 
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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  • V. I. Burenkov
    • 1
  • M. Lanza de Cristoforis
    • 1
  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversità di PadovaPadovaItaly

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