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

Abstract

Let n≥2 and $1\leq q<p><\fz$. We prove that if Ω⊂Rn is a Sobolev (p,q)-extension domain, with additional capacitory restrictions on boundary in the case q≤n−1, n>2, then |∂Ω|=0. In the case 1≤q0.</p>