Unique continuation for parabolic operators

Abstract

It is shown that if a function u satisfies a backward parabolic inequality in an open set Ω ⊂ Rn+1 and vanishes to infinite order at a point (x0, t0) in Ω, then u(x, t0)=0 for all x in the connected component of x0 in Ω∩(Rn × {t0}).