## Abstract

Let n ≥ 2 and 1 ≤

(

*q*<*p*< ∞. We prove that if Ω ⊂ R^{n}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.Original language | English GB |
---|---|

State | Published - 14 Dec 2020 |

## Keywords

- math.AP
- math.FA