Question: Consider $\Omega$ a open and bounded set.

Let $u \in H^{1}\_0(\Omega)$ a continuous function. is true that $lim\_{x \rightarrow y} u(x) = 0$ for $y \in \partial \Omega$ ? I dont know how to prove this.... Someone can give me a help to prove this affirmation ? 

thanks in advance

Answer: 
$$C\_G(H)=\{g\in G:gh=hg\;\forall h\in H\}.$$

So what are the elements of $G$ which commute with every element of the centre? By definition, it's all of them.
$C\_G(H)$ = "The things in $G$ which commute with everything in $H$". So which things in $G$ commute with the center of $G$? By the definition of the center, it better be everything.