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

Let $\Omega$ be a bounded open subset of $\mathbb{R}^ n$ . Prove that there exists a constant $C$, depending only on $\Omega$, such that
$$\max |u| \leq C (\max_{\partial \Omega }|g|+\max_{\overline{\Omega} }|f|),$$
where $u$ is a solutions of the PDE
$$-\Delta u=f$$ with $u=g$ on $\partial \Omega$.