Unique continuation for the Schrödinger equation with gradient term

Abstract

We obtain a unique continuation result for the differential inequality $|(i{\partial }_t+\Delta )u|\le |Vu|+|W\cdot \nabla u|$ by establishing $L^2$ Carleman estimates. Here, $V$ is a scalar function and $W$ is a vector function, which may be time-dependent or time-independent. As a consequence, we give a similar result for the magnetic Schrödinger equation.

arXiv commentTo appear in Proc. Amer. Math. Soc., 8 pages