Strong minimum principle for elliptic operators
= Strong minimum principle for elliptic operators
Let $L$ be uniformly elliptic with bounded coefficients and nonpositive zeroth-order coefficient. If $u\geq0$, $Lu\leq0$, and $u$ vanishes at an interior point of a connected domain, then $u$ vanishes identically. This is the minimum form of the <Strong maximum principle for harmonic functions>[strong maximum principle].