Uniform stability of the Dirichlet spectrum for rough outer perturbations
Bruno Colbois, Alexandre Girouard, Mette Iversen · Journal of Spectral Theory · 2013
The goal of this paper is to study the Dirichlet eigenvalues of bounded domains \Omega\subset\Omega' . With a local spectral stability requirement on \Omega , we show that the difference of the Dirichlet eigenvalues of \Omega' and \Omega is explicitly controlled from above in terms of the first eigenvalue of \Omega'\setminus\bar{\Omega} and of geometric constants depending on the inner domain \Omega . In particular, \Omega' can be an arbitrary bounded domain.