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 Nov30 awarded Yearling Oct9 awarded Notable Question Jul2 awarded Curious Jun11 awarded Popular Question Apr9 awarded Popular Question Feb6 awarded Popular Question Nov30 awarded Yearling Nov15 awarded Popular Question May20 accepted What is the Sobolev Lemma? May19 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 $||u|| = \max_{x \in \bar{\Omega}}{|u|} + \max_{x \in \bar{\Omega}}{|\nabla u|}$ May17 comment What is the Sobolev Lemma? Yes, I guess so May17 comment What is the Sobolev Lemma? $s$ is how many derivatives you are considering. I don't know how you do this... May17 comment What is the Sobolev Lemma? Well, not really I just realized that this result if for the whole of $\mathbb{R}^N$. May17 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. May17 comment What is the Sobolev Lemma? Should be in $W^{1,\infty}$ I suppose. May17 asked What is the Sobolev Lemma? May16 answered Find vectors vertical to given vectors with certain length May13 comment asymptotic behavior of the solution to an ODE Cheers, that is very useful. On second thought I think I need a uniform estimate and your calculation seems to be very useful. May13 accepted asymptotic behavior of the solution to an ODE May12 comment asymptotic behavior of the solution to an ODE Both, if possible.