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 $\Omega_\varepsilon$ as $\varepsilon\to0$. 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 [F. Antoci and M. Prizzi, Reaction-diffusion equations on unbounded thin domains, Topol. Methods Nonlinear Anal. 18 (2001), 283-302] in the flat squeezing case.