2
$\begingroup$

Let $\Omega\subset\mathbb{R}^n$ be an limited open set of class $C^1$ and $1\leq p<\infty$. Show that $\bigcap_{m=0}^{\infty}W^{m,p}(\Omega)=C^{\infty}(\overline{\Omega}).$

  • 0
    The inclusion $\supset$ I used the fact that the support is compact in $\overline{\Omega}$. But the other inclusion is not clear, since we have $\Omega$ of $C^1$ class. I dont´t know how to use Morrey's Inequality. :(2012-07-08

0 Answers 0