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

Let n≥2 and 1≤q<p<∞. We prove that if Ω⊂Rⁿ is a Sobolev (p,q)-extension domain, with additional capacitary restrictions on the boundary in the case q≤n−1, n>2, then |∂Ω|=0. In the case 1≤q<n−1, we give an example of a Sobolev (p,q)-extension domain with |∂Ω|>0.