I'm trying to solve the following problem:
Given a domain $\Omega \subset R^n$, consider nthe dirichlet problem for the Leplace equation, that is: $$ ∆u = 0 \: in \: x \in \Omega \\ u(x) = 0 \: in \: x \in \Omega $$
Show that if there is a solution $u \in C^2(\Omega)$ is exactly zero