 Gradient maximum principle for harmonic functions (source code)

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= Gradient maximum principle for harmonic functions
{title2=$\sup_\Omega|Dw|=\sup_{\partial\Omega}|Dw|$}

For a <harmonic function> $w$ smooth inside a bounded domain and $C^1$ on its closure, $\Delta|Dw|^2=2|D^2w|^2\geq0$. The <weak maximum principle for elliptic operators> and continuity of the <gradient> imply $\sup_\Omega|Dw|=\sup_{\partial\Omega}|Dw|$.

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