I have two questions:
Is $C(0,1)$ dense in $H^2(0,1)$? Yes or no? Could you give me a proof or an explanation?
$C^\infty_c(\Omega) = C^\infty_0(\Omega)$? from the different textbooks, I see that the spaces $C^\infty_0(\Omega)$ consists of all those functions in $C^\infty(\Omega)$ that have compact support in $\Omega$. But it seems that $C^\infty_c(\Omega)$ has the same meaning. the little $c$ means compact support? or it depends on the set $\Omega$?
Please help me. Thanks.