# Density of $C^\infty(\overline{\Omega})$ in $W^{k,2}(\Omega)$

First, $$\Omega\subseteq \mathbb{R}^n$$ and $$\Omega=\prod_{i=1}^n\left(a_i,b_i\right).$$ I know that the space of test functions $$C^\infty_c(\Omega)$$ is indeed dense in $$W^{k,2}(\Omega)$$. Is there anyway to use that result to prove that $$C^\infty(\overline{\Omega})$$ is dense in $$W^{k,2}(\Omega)$$?

• And if is not possible to use that result, is there another result that can be used? – mathgirl796 May 26 at 4:58