Im a student of this world learning about Sobolev spaces right now and I recently posted a question which was closed and I got confused by that because I didnt received any feedback. I thought maybe it was closed because the statement in that question was just wrong. I want to know if it was right or wrong.
I stated that one can ALWAYS (not only in certain domains) extend functionsin $W^{k,p}_0(\Omega)$ to $W^{k,p}(\mathbb{R}^n)$ with its zero extention.
I know that the converse is problematic i.e. we cant just take something from $W^{k,p}(\mathbb{R}^n)$ restrict it on $\Omega$ to obtain something from $W^{k,p}_0(\Omega)$. But the other implication is certainly true I think.
A quick feedback whether Im right or wrong would be great.