Uniform stability of the Dirichlet spectrum for rough outer perturbations (Q398188)

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