can someone help me out and name a good source where the following statement ist proven?

$C^\infty_0(\Omega)$ is dense in $W^{1,p}_0(\Omega)$ with $\Omega \subset \mathbb{R}^n$ being an open, bounded domain with continuous boundary $\partial \Omega$.

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    $\begingroup$ Do you know Evans book on PDE? This proof is included in Chapter 4. $\endgroup$ – Joaquin San May 19 at 12:59
  • $\begingroup$ Are you sure? In the chapter "4. other ways to represent solutions"? Without reading the whole chapter I am a bit skeptical since sobolev spaces are in only introduced in the following chapter 5... At least in my version of the book. $\endgroup$ – superdave99 May 19 at 13:04
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    $\begingroup$ For me (and many others), this is the definition of $W_0^{1,p}(\Omega)$. Which definition do you use? $\endgroup$ – gerw May 19 at 14:40
  • $\begingroup$ Ohh correct. Chapter 5 heh $\endgroup$ – Joaquin San May 20 at 14:09

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