Uniform stability of the Dirichlet spectrum for rough outer perturbations

Bruno Colbois; Alexandre Girouard; Mette Iversen

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arXiv · 1206.2616

Uniform stability of the Dirichlet spectrum for rough outer perturbations

Bruno Colbois·Alexandre Girouard·Mette Iversen

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Abstract

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

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BibTeX RIS

Bruno Colbois, Alexandre Girouard, Mette Iversen. 2012-06-12. Uniform stability of the Dirichlet spectrum for rough outer perturbations. https://arxiv.org/abs/1206.2616

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