Carleman inequalities and inverse problems for the Schrodinger equation

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.This work was performed while the third author was visiting the CMM, UMI CNRS 2807.The second author was partially supported by FONDECYT grant 1061263. The first and second authors acknowledge ECOS C04E08 grant