Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

share|improve this question
    
Have you shown that $C^{\infty}(\overline{\Omega})$ is contained in the intersection, using the fact that the open set is bounded? –  Davide Giraudo Jul 7 '12 at 20:36
    
For the other inclusion you can think at the Morrey's inequality –  Giuseppe Negro Jul 7 '12 at 20:42
    
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. :( –  user23069 Jul 8 '12 at 20:40
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.