Inverse problems for the Schrödinger equation via Carleman inequalities with degenerate weights

(Baudouin and Puel 2002 Inverse Problems 18 1537–54), investigated some inverse problems for the evolution Schrödinger equation by means of Carleman inequalities proved under a strict pseudoconvexity condition. We show here that new Carleman inequalities for the Schrödinger equation may be derived under a relaxed pseudoconvexity condition, which allows us to use degenerate weights with a spatial dependence of the type ψ(x) = x ⋅ e, where e is some fixed direction in . As a result, less restrictive boundary or internal observations are allowed to obtain the stability for the inverse problem consisting in retrieving a stationary potential in the Schrödinger equation from a single boundary or internal measurement.