The volume of the boundary of a Sobolev $(p,q)$-extension domain

Pekka Koskela, Alexander Ukhlov, Zheng Zhu

Let $n\ge 2$ and $1\leq q<p<\fz$. We prove that if $\Omega \subset {\mathbb{R}}^n$ is a Sobolev $(p,q)$-extension domain, with additional capacitory restrictions on boundary in the case $q…