# Pointwise estimate for solutions of the laplace equation on bounded domains

$$\max |u| \leq C (\max_{\partial \Omega }|g|+\max_{\overline{\Omega} }|f|), $$

where $u$ is a solutions of the PDE

$$ -\Delta u=f $$ with $u=g$ on $\partial \Omega$.

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Erdos

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