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 capacitory restrictions on 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.