Reference request for the existence of Sobolev traces on Lipschitz domains

Question

Let $\Omega \subseteq \mathbb R^d$ be a bounded Lipschitz domain. Then it is well known that the trace operator $$ \operatorname{tr} \colon W^{1, 1}(\Omega) \to L^1(\partial \Omega)$$ is well-defined and bounded. However, I was unable to find a citable reference for this fact. The references I found either focus on the $L^2$-setting, assume more regularity of the boundary of $\Omega$ (mostly $C^1$-boundary) or are kind of obscure. Another reference, is the seminal paper of Gagliardo for that fact, the drawback of this reference being that it is written in Italian. Nonetheless, I cannot imagine that there is not a well-cited book serving as a standard reference for PDEs or Sobolev spaces that contains the result in the above form. So it would be very nice if someone would know a reference including the result. Thanks in advance!

Answer 1

This is Theorem 15.10 in Giovanni Leoni's "A first course in Sobolev Spaces".