Fractional Sobolev spaces and extension by zero

Question

The all-wise Wikipedia suggest (https://en.wikipedia.org/wiki/Sobolev_space#Extension_by_zero) that for $s > 1/2$ any function from $H^s_0(\Omega)$ can be extended by zero to whole $\mathbb{R}^n$ (with the extension being in $H^s(\mathbb{R}^n)$) under some mysterious condition, namely $s \neq \mbox{integer} + 1/2$.

I saw this proposition in a couple of papers, but always without a proof or reference.

Does anyone has an idea where it comes from?

Thank you in advance

Answer 1

The answer is blowin' in the wind... unless $\Omega$ is Lipschitz domain, in which case the proof can be found in the book of`W. McLean "Strongly Elliptic Systems and Boundary Integral Equations".

I would also recommend the paper "Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains" by Sergey Mikhailov which is available in the net and has well documented references.

Good luck everyone!