A trace embedding for fractional Sobolev space

Question

I was reading a paper. There I found for a Lipschitz domain $\Omega \subset \mathbb{R}^n, n\geq 2$, the following holds: there is a continuous trace operator from $H^\beta (\Omega)$ to $L^2 (\partial \Omega)$, for some $\beta \in (\frac{1}{2},1)$. The authors did not cite any source for such a result. Does anyone know any source where I can find this result?

Answer 1

The trace theorem (as well as extension theorem) for Lipschitz domains can be found, e.g., in Theorem 3.37 pp 102 for $\frac{1}{2}<\beta \le 1$ (just take $k=1$) in the following book:

McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge, UK (2000).

PS: A stronger result holds for the range $\frac{1}{2}<\beta <\frac{3}{2}$, see Theorem 3.38.