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Is $C_0^\infty $ dense in $W^{m,p}$?

Here $C_0^\infty$ = $C_c ^ \infty$ : $C^\infty$ with compact supports, and $W^{m,p}$ : Sobolev spaces.

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    yes it is indeed .2012-06-10
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    @Ananda Thank you Ananda, is the proof of this statement difficult?2012-06-10
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    You can find the proof of it in Evans PDE. It's not that difficult although i found it difficult when i saw it first .2012-06-10
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    You mean $C_0^{\infty}(\Bbb R^d)$, or of a particular open set?2012-06-10
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    Davide makes a good point: the density depends on the domain, as well as on the exponents $m, p$.2012-06-10
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    @DavideGiraudo How about the situation $C_0^\infty (\mathbb R^d )$ with $ W^{1,2}$ ?2012-06-10
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    It works even for $p\in [1,+\infty)$, the proof is standard, first reducing to the case $u$ with a bounded singular support, then taking the convolution with a mollifier.2012-06-12
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    I guess so.....2017-09-30
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    @HighGPA Your name is funny haha2018-04-27
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    @KitWong My name used to be LowGPA, but someone suggested me to change it...2018-04-27

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