Inverse Scattering for Schrödinger-Type Operators with Interface Conditions Across Smooth Surfaces

We consider direct and inverse scattering for the Laplace-Beltrami operator with electromagnetic potentials in domains with smooth surfaces upon which we impose interface conditions. The boundary conditions used encompass physical models of imperfect transmission arising in acoustics, quantum scattering, semiconductors, and geophysics. We prove uniqueness of the location of the surfaces and the interface conditions from the fixedenergy scattering amplitude. If the surface encloses a compact region, we also prove uniqueness of the Dirichlet-to-Neumann operator at the boundary of the obstacle.