I have the following question:
Let $\Sigma$ an a surface inside of an open domain $\Omega\subseteq\mathbb{R}^3$, where $\Sigma$ divides $\Omega$ in 2 open domains (for example: $\Sigma$ could be a plane).
Let $g\in H^{1/2}(\Sigma)$. How can I probe that exists $u\in H^1(\Omega\setminus\Sigma)$ such that
$\|u\|_{H^1(\Omega)}\leq C\|g\|_{H^{1/2}(\Sigma)}$?
where $C$ is a constant.
Thanks in advance!