Resolvent convergence for Laplace operators on unbounded curved squeezed domains

Abstract

We establish a resolvent convergence result for the Laplace operator on certain classes of unbounded curved squeezed domains $\Omega_\eps$ as $\eps\to0$. As a consequence, we obtain Trotter-Kato-type convergence results for the corresponding family of $C^0$-semigroups. This extends previous results obtained by Antoci and Prizzi in \cite{\rfa{AP}} in the flat squeezing case.