A Hilbert space which involves the boundary norm and interior norm?

Question

Let $\Omega\subset \mathbb{R}^n$ be a bound domain with enough smooth boundary, does there exist a Hilbert space $H$ on $\Omega$ such that the norm is given by $$||f||^2=\int_{\Omega}|f|^2dx+\int_{\partial\Omega}|f|^2d\sigma,\ \forall f\in L^2(\overline{\Omega}).$$