The goal of this paper is to study the Dirichlet eigenvalues of bounded domains . With a local spectral stability requirement on , we show that the difference of the Dirichlet eigenvalues of and is explicitly controlled from above in terms of the first eigenvalue of and of geometric constants depending on the inner domain . In particular, 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. 575–599DOI 10.4171/JST/57