Spectral stability estimates for elliptic operators subject to domain transformations with non-uniformly bounded gradients (Q2902663)

The paper deals with uniformly elliptic operators subject to Dirichlet or Neumann homogeneous boundary conditions over a domain \(\Omega \) in \(\mathbb R^{N}\). Considering deformations \(\varphi (\Omega)\) of \(\Omega\) obtained by means of a locally Lipschitz homeomorphism \(\varphi\), the authors estimate the variation of the eigenfunctions and eigenvalues upon variation of \(\varphi\), obtaining in this way a general stability result without assuming uniform upper bounds for the gradients of the maps \(\varphi\). As an application, estimates on the rate of convergence are obtained for the eigenvalues and eigenfunctions when a domain with an outward cusp is approximated by a sequence of Lipschitz domains.