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



Fractional Sobolev spaces and extension by zero
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!


