Timeline for Variation on the Sobolev space $H^1_0$

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Nov 5, 2013 at 14:45	vote	accept	timur
Nov 4, 2013 at 18:43	comment	added	Jean Van Schaftingen		@timur: If $\Omega$ is bounded, then $u \in C_0 (\Omega)$ if and only if $u \in C_0 (\bar{\Omega})$ and $u\vert_{\partial \Omega} = 0$. If $\Omega$ is not bounded, then $u \in C_0 (\Omega)$ if and only if $u \in C_0 (\bar{\Omega})$, $u\vert_{\partial \Omega} = 0$ and $\lim_{\vert x \vert \to \infty} u (x) = 0$.
Nov 4, 2013 at 14:14	comment	added	timur		Thanks a lot! Just to be sure, if $\Omega$ is bounded open and $u\in C(\bar\Omega)$ with $u\|_{\partial\Omega}=0$, then $u\in C_0(\Omega)$ by your definition of $C_0$. Is my understanding correct?
Nov 3, 2013 at 13:14	history	answered	Jean Van Schaftingen	CC BY-SA 3.0