Carleman inequalities and inverse problems for the Schrodinger equation

Abstract

In this Note, we derive new Carleman inequalities for the evolution Schrodinger equation under a weak pseudoconvexity condition, which allows us to use weights with a linear spatial dependence. As a result, less restrictive boundary or internal observation regions may be used to obtain the stability for the inverse problem consisting in retrieving a stationary potential in the Schrodinger equation from a single boundary or internal measurement, respectively.