Space like strong unique continuation for sublinear parabolic equations
Agnid Banerjee, Ramesh Manna · Journal of the London Mathematical Society · 2020
In this paper, we establish space like strong unique continuation property 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 in (Ruland, J. Differential Equations 265 (2018) 6009–6035) for elliptic sublinear equations with analogous structure conditions. Similar to that in (Ruland, J. Differential Equations 265 (2018) 6009–6035), this is accomplished via a new L 2 − L 2 type Carleman estimate for a class of sublinear parabolic operators.