trace of an $H^1$ function is in $H^\frac{1}{2}$

Question

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 $H^\frac{1}{2}(\partial \Omega)$.

Answer 1

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.

Answer 2

In some books, $H^{1/2}$ is defined to be the trace of $H^{1}$ functions, for example in Girault, V.; Raviart, P.-A., Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms