Stable determination of coefficients in the dynamical Schrödinger equation in a magnetic field. (13th March 2017) - Bellassoued, Mourad
Abstract: In this paper we consider the inverse problem of determining, on a compact Riemannian manifold, the electric potential or the magnetic field in a Schrödinger equation via Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the magnetic Schrödinger equation. We prove in dimension n ⩾ 2 that the knowledge of the Dirichlet-to-Neumann map for the Schrödinger equation uniquely determines the magnetic field and the electric potential and we establish Hölder-type stability.