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] $. I tried partial differentiation, but it doesnt work.
Some kind of trace inequality
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$\begingroup$
inequality
estimation
trace
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0You'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. – 2012-12-03
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0For which $u$ do you want such an inequality? – 2012-12-03
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0For all $u \in H^1(\Omega)$. – 2012-12-03