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Let $u$ be a harmonic function and $\Omega$ be a convex domain. Then is the following true? $$ \frac{\int_{\Omega} |\nabla u|^2 \,dx}{\int_{\partial \Omega} |\nabla u|^2 \,d\sigma} \leq \frac{\int_{B} |\nabla u|^2 \,dx}{\int_{\partial B} |\nabla u|^2 \,d\sigma} $$ where $B$ is the ball such that $|B| = |\Omega|$.

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