TITLE: trace of an $H^1$ function is in $H^\frac{1}{2}$
QUESTION [6 upvotes]: Let $\Omega$ be a bounded open set in $\mathbb{R}^n$ with smooth boundary.  Let $u \in H^1(\Omega)$.  I would like a reference for the fact that the trace of $u$ on $\partial \Omega$ is in $H^\frac{1}{2}(\partial \Omega)$.

REPLY [4 votes]: n case anyone is curious, the answer seems to be at mipa.unimes.fr/preprints/MIPA-Preprint05-2011.pdf, Proposition 4.5.  This is an excellent introduction to fractional-order Sobolev spaces.