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We consider the Dirichlet Laplacian $\mathcal{A}_\varepsilon=-\Delta$ in thedomain $\Omega\setminus\bigcup_i K_{i\varepsilon}\subset\mathbb{R}^n$ withholes $K_{i\varepsilon}$ and the Schr\"{o}dinger operator$\mathcal{A}=-\Delta+V$ in $\Omega$ where $V$ is the $L^n(\Omega)$ limit of thedensity of the capacities $\operatorname{cap}(K_{i\varepsilon}).$ Strongresolvent convergence for many $V\in W^{-1,\infty}(\Omega)$ was studied by theauthor. In this paper, we study about convergence rate for$\mathcal{A}_\varepsilon\to\mathcal{A}$ in norm resolvent sense. The case forwhich $V$ is a constant is studied by Andrii Khrabustovskyi and Olaf Post.

Convergence rate of Dirichlet Laplacians on domains with holes to the Schr\"{o}dinger operator with $L^p$ potential