Let $\Omega\subset\mathbb{R}^n$ be an limited open set of class $C^1$ and $1\leq p<\infty$. Show that $\bigcap_{m=0}^{\infty}W^{m,p}(\Omega)=C^{\infty}(\overline{\Omega}).$
An exercise about Sobolev Spaces
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sobolev-spaces
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0The inclusion $\supset$ I used the fact that the support is compact in $\overline{\Omega}$. But the other inclusion is not clear, since we have $\Omega$ of $C^1$ class. I dont´t know how to use Morrey's Inequality. :( – 2012-07-08