Determining an Unbounded Potential from Cauchy Data in Admissible Geometries

In [] anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. In particular, it was proved that a bounded smooth potential in a Schrodinger equation was uniquely determined by the Dirichlet-to-Neumann map in dimensions n = 3. In this article we extend this result to the case of unbounded potentials, namely those in L n/2. In the process, we derive L p Carleman estimates with limiting Carleman weights similar to the Euclidean estimates of Jerison and Kenig [] and Kenig et al. [].