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What is the trick, to prove $\| u\|_{L^2(\Gamma)} \leq k \frac{1}{r}\| u\|_{L^2(\Omega)} + r \| \nabla u\|_{L^2(\Omega)} $ ? $\Gamma$ is one side of $\Omega:= [0,r] \times [0,r] $. I tried partial differentiation, but it doesnt work.

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You'll probably want to add more tags to this to get it more attention. "inequality" is a bit vague and doesn't reflect the content well. – Simon Hayward Dec 3 '12 at 15:35
For which $u$ do you want such an inequality? – Davide Giraudo Dec 3 '12 at 15:45
For all $u \in H^1(\Omega)$. – JamesB Dec 3 '12 at 15:59

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