A remark on a vanishing property for viscosity solutions of fully nonlinear parabolic equations

We make the observation that, under some natural conditions on FF (stated in (A)–(C) in the main text), if a viscosity solution of the fully nonlinear parabolic equation F(D2u,Du,u)−ut=0 vanishes to infinite order at (x0,t0)(x0,t0), then there is a small spatial neighborhood Br0(x0)×{t0}Br0(x0)×{t0} of (x0,t0)(x0,t0) in which uu vanishes identically. The proof is inspired in an essential way by the ideas employed in the recent paper Armstrong and Silvestre (2011) [2], where the unique continuation property for fully nonlinear elliptic equations was established.