Laplace Equation

I'd like something to compare my answer to before submission.

I'd like something to compare my answers to before submission. 

Let $\Omega$ be a bounded domain in $\mathbb R^n$ with smooth boundary. Assume that $u \in C^2(\bar \Omega) \cap H_0^1 (\Omega)$ be a strong solution to with $u=0$ on $\partial \Omega$. Show that $u \...

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{\Om...