Operator estimates for the crushed ice problem

Andrii Khrabustovskyi, Olaf Post

Let ${\Delta }_{{\Omega }_{\epsilon }}$ be the Dirichlet Laplacian in the domain ${\Omega }_{\epsilon }:=\Omega \setminus \left({\cup }_i{D}_{i\epsilon }\right)$. Here $\Omega \subset {\mathbb{R}}^n$ and $\{D_{i \varepsil…