Weak form: a subharmonic function u (Δu ≥ 0) on a bounded domain attains its supremum on the boundary. Strong form (E. Hopf 1927): if u attains the supremum at an interior point of a connected Ω, then u is constant. Parabolic analogue:…
Weak form: a subharmonic function u (Δu ≥ 0) on a bounded domain attains its supremum on the boundary. Strong form (E. Hopf 1927): if u attains the supremum at an interior point of a connected Ω, then u is constant. Parabolic analogue:…