Solution
= Solution
For any rotation $R$ about the centre, $\phi_R(x)=\phi(Rx)$ satisfies the same equation and the same Dirichlet data because $V,f,g$ are rotationally invariant. Uniqueness from part (a) gives $\phi_R=\phi$ for every $R$. Thus $\phi$ is constant on spheres and is a <function> of $r$ alone.