Stable determination of a vector field in a non-Self-Adjoint dynamical Schrödinger equation on Riemannian manifolds

Abstract

<p style='text-indent:20px;'>This paper deals with an inverse problem for a non-self-adjoint Schrödinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical Dirichlet-to-Neumann map. We establish in dimension <inline-formula><tex-math id="M1">\begin{document}$ n\geq2 $\end{document}</tex-math></inline-formula>, an Hölder type stability estimate for the inverse problem under study. The proof is mainly based on the reduction to an equivalent problem for an electro-magnetic Schrödinger equation and the use of a Carleman estimate designed for elliptic operators.