Let $\Omega$ be a Lipschitz domain in $\mathbb{R}^d$, and let $\Gamma$ be an open subset of $\partial \Omega$ (not necessarily the whole $\partial \Omega$). I cannot find a result that proves the existence of a linear continuous extension operator $T$ from $H^{1/2}(\Gamma)$ to $H^1(\Omega)$, that is $\|T(g)\|_{H^{1}(\Omega)} \leq C \|g \|_{H^{1/2}(\Gamma)}$ for all $g \in H^{1/2}(\Gamma)$.
Could anyone help me find it?