Inverse problems for a Schrödinger equation defined in an unbounded domain
In this talk, we discuss the stability issue for the inverse problem of determining the electric potential appearing in a Schrödinger equation defined on an infinite cylindrical waveguide. We consider both results of stability from full and partial boundary measurements associated with the so-called Dirichlet-to-Neumann map. In the presence of the magnetic potential, a second problem is considered for which we prove that the electric potential and the magnetic field depend stably on the global and partial Dirichlet-to-Neumann maps. Our approach combines construction of complex geometric optics solutions and Carleman estimates suitably designed for our stability results stated in an unbounded domain.