I've been looking for a while in different Functional Analysis books such as Luc Tartar, Jean Pierre Aubin and Brezis but couldn't find the proof of the density of $C_0^\infty(\overline \Omega)$ in $H(\operatorname{div};\Omega)$ when $\Omega$ is an open bounded subset of $\mathbb R^n$ with Lipschitz boundary $\Gamma:=\partial \Omega$. Can you recommend me a good source to check it?
2026-03-27 10:10:06.1774606206
$C_0^\infty(\overline \Omega)$ is dense in $H(\operatorname{div};\Omega)$
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