Maximum-Minimum principle in partial differential equation

Question

If $u(x,y)$ is harmonic on a bounded domain $D$ and continuous on $D \cup B$ where $B$ is the boundary of domain $D$. Then prove that $u(x,y)$ attains its minimum on the boundary $B$.

Answer 1

You can find a proof that exploites the mean value formula in Evans book Partial Differential Equations (Theorem 4, in chapter 2.2, pg 27).