Space like strong unique continuation for sublinear parabolic equations: SPACE LIKE STRONG UNIQUE CONTINUATION

In this paper, we establish space like strong unique continuation property (sucp) for uniformly parabolic sublinear equations under appropriate structural assumptions. Our main result Theorem 1.1 constitutes the parabolic counterpart of the strong unique continuation result recently established by Ruland in [Ru] for analogous elliptic sublinear equations. Similar to that in [Ru], this is accomplished via a new $L^{2}-L^{2}$ type Carleman estimate for a class of sublinear parabolic operators.