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Neumann problem on a convex domain

Let $\Omega$ be a convex open bounded subset of $\mathbb R^n$ and let $u$ be the solution of $$ \begin{cases} ∆ u=1\quad\text{in $\Omega$,} \\ \frac{\partial u}{\partial \nu}=\frac{\vert \Omega\vert_n …
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