Convergence rate of Dirichlet Laplacians on domains with holes to the Schrödinger operator with $L^p$ potential

We consider the Dirichlet Laplacian ${\mathcal{A}}_{\epsilon }=-\mathrm{\Delta }$ in the domain $\mathrm{\Omega }\setminus {\bigcup }_i{K}_{i\epsilon }\subset {\mathbb{R}}^n$ with holes $K_{i\epsilon }$ and the Schrödinger operator $\mathcal{A}=-\mathrm{\Delta }+V$ in $\mathrm{\Omega }$ where $V$ is the $L^n(\mathrm{\Omega })$ limit of the density of the capacities $\mathrm{cap}(K_{i\epsilon })\mathrm{.}$ Strong resolvent convergence for many $V\in W^{-1,\mathrm{\infty }}(\mathrm{\Omega })$ was studied by the author. In this paper, we study about convergence rate for ${\mathcal{A}}_{\epsilon }\to \mathcal{A}$ in norm resolvent sense. The case for which $V$ is a constant is studied by Andrii Khrabustovskyi and Olaf Post.