Solution
= Solution
\b[True.] Continuity and compactness give a maximum of $\phi$ on $\overline\Omega$. At an interior maximum the <Hessian matrix> is negative semidefinite, so its trace satisfies $\Delta\phi\leq0$, contradicting $\Delta\phi>0$. The maximum must therefore occur on $\partial\Omega$. This is the strict form of the <maximum principle for subharmonic functions>.