Stability estimates for partial data inverse problems for Schrodinger operators in the high frequency limit

We discuss the partial data inverse boundary problem for the Schroedinger operator at a fixed frequency on a bounded domain in the Euclidean space, with impedance boundary conditions.  Assuming that the potential is known in a neighborhood of the boundary, the knowledge of the partial Robin-to-Dirichlet map along an arbitrarily small portion of the boundary determines the potential uniquely, in a logarithmically stable way. In this talk we show that the logarithmic stability can be improved to the one of Holder type in the high frequency regime. Our arguments are based on boundary Carleman estimates for semiclassical Schrodinger operators acting on functions satisfying impedance boundary conditions. This is joint work with Gunther Uhlmann.