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Apr
3
awarded  Nice Question
Mar
18
awarded  Notable Question
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30
awarded  Yearling
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22
awarded  Popular Question
Sep
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awarded  Notable Question
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awarded  Curious
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May
20
accepted What is the Sobolev Lemma?
May
19
comment What is the Sobolev Lemma?
Thank you! So how does this imply my result exactly. I know that with $m=1$, $\nabla u$ is continuous and therefore bounded in the compact set $\bar{\Omega}$. What norm do you define on $C^m(\bar{\Omega})$? Something like $||u|| = \max_{x \in \bar{\Omega}}{|u|} + \max_{x \in \bar{\Omega}}{|\nabla u|}$
May
17
comment What is the Sobolev Lemma?
Yes, I guess so
May
17
comment What is the Sobolev Lemma?
$s$ is how many derivatives you are considering. I don't know how you do this...
May
17
comment What is the Sobolev Lemma?
Well, not really I just realized that this result if for the whole of $\mathbb{R}^N$.
May
17
comment What is the Sobolev Lemma?
I think I might have found the relevant theorem after all. It's Corollary 9.13 in Brezis's book FA, SS and PDEs (page 284). It's strange that I could not find it in Adams being that its a more thorough account of Sobolev's Spaces.
May
17
comment What is the Sobolev Lemma?
Should be in $W^{1,\infty}$ I suppose.