Suppose $u\in W^{1,1}$ and $\partial u$ is $C^1$. I want to prove the following: $\int_{\partial\Omega}|u-\bar u|\leq A\int_{\Omega}|\nabla u|$, where $\bar u=\dfrac{1}{|\Omega|}\int_{\Omega}u$ and $A>0$. Note that unlike Poincare inequality, the left integral is over $\partial\Omega$ and not $\Omega$. How can I do that?
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Best thing you can do is improve this question and add what your thoughts are. What do you think will help? Which theorems/lemmas/formulas do you think you need, but you maybe don't see how to apply them, ... . Otherwise your question can be downvoted & closed for off-topic with the additional comment that you need to provide context which ideally include your thoughts about the problem and ways you tried to solve the problem. – Pedro Apr 07 '15 at 12:03
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There is no need to ask the same question. Just follow the instructions given for the closure of the last one and then hit the button reopen. Take a look in @Pedro's comment. – Tomás Apr 07 '15 at 12:24
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@Thomas You need 250 reputation to cast a reopen vote on your own question. – Pedro Apr 07 '15 at 12:25
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Edit it and ask on meta to reopen, or just edit it and I will vote to reopen. – Tomás Apr 07 '15 at 12:28
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I edited the one which is on hold. Please vote to reopen. – Aron Apr 07 '15 at 13:55