JournalsjstVol. 3, No. 4pp. 575–599

Uniform stability of the Dirichlet spectrum for rough outer perturbations

  • Bruno Colbois

    Université de Neuchâtel, Switzerland
  • Alexandre Girouard

    Université Laval, Quebec, Canada
  • Mette Iversen

    University of Bristol, UK
Uniform stability of the Dirichlet spectrum for rough outer perturbations cover
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Abstract

The goal of this paper is to study the Dirichlet eigenvalues of bounded domains ΩΩ\Omega\subset\Omega'. With a local spectral stability requirement on Ω\Omega, we show that the difference of the Dirichlet eigenvalues of Ω\Omega' and Ω\Omega is explicitly controlled from above in terms of the first eigenvalue of ΩΩˉ\Omega'\setminus\bar{\Omega} and of geometric constants depending on the inner domain Ω\Omega. In particular, Ω\Omega' can be an arbitrary bounded domain.

Cite this article

Bruno Colbois, Alexandre Girouard, Mette Iversen, Uniform stability of the Dirichlet spectrum for rough outer perturbations. J. Spectr. Theory 3 (2013), no. 4, pp. 575–599

DOI 10.4171/JST/57