is the follwing true: Let $I\subseteq \mathbb{R}^n$ open, bounded. Then $C^2(\overline{I},\mathbb{R}^n)$ is dense in $W^{1,p}(I,\mathbb{R}^n)$ with respect to the $W^{1,p}$-norm? If yes, do you have a reference?
Thanks in advance.
denseness in Sobolev spaces
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functional-analysis
sobolev-spaces
1 Answers
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This is theorem 8.7 in Brezis: Functional analysis, Sobolev spaces and partial differential equations.
Brezis starts with Sobolev spaces on intervalls, which makes it quite accessible for a start.