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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 $W^{k,2}(\Omega)$?

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

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