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

Let $n\ge 2$ and $1\le q<p<\text{fz}$. We prove that if $\Omega\subset\mathbb R^n$isaSobolev$(p, q)$-extension domain, with additional capacitory restrictions on boundary in the case $q\le n-1$, $n>2$, then $\mathrm{\mid }\mathrm{\partial }\mathrm{\Omega }\mathrm{\mid }=0$. In the case $1\le q<n-1$, we give an example of a Sobolev $(p,q)$-extension domain with $\mathrm{\mid }\mathrm{\partial }\mathrm{\Omega }\mathrm{\mid }>0$.