Global unique continuation from a half space for the Schr?dinger equation

摘要

We obtain a global unique continuation result for the differential inequality |(i?_t + △)u| ≤ |V(x)u| in ?~(n+1) This is the first result on global unique continuation for the Schr?dinger equation with time- independent potentials V(x) in ?~n. Our method is based on a new type of Carleman estimates for the operator i?_t + Δ on ?~(n+1). As a corollary of the result, we also obtain a new unique continuation result for some parabolic equations.