Apply the weak <weak maximum principle for elliptic operators> to the <harmonic function> $\phi$ and to $-\phi$. Their boundary maxima are both zero, giving $\phi\leq0$ and $\phi\geq0$ on the closure. Consequently \b[$\phi\equiv0$].

Solution

Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 1 / 2I / iv / Solution

 Solution (source code)