STABLE DETERMINATION OF A VECTOR FIELD IN A NON-SELF-ADJOINT DYNAMICAL SCHRODINGER EQUATION ON RIEMANNIAN MANIFOLDS

This paper deals with an inverse problem for a non-self-adjoint Schrodinger 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 n >= 2, an Holder 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 Schrodinger equation and the use of a Carleman estimate designed for elliptic operators.

Automated summary

This paper addresses an inverse problem for a non-self-adjoint Schrodinger equation on a compact Riemannian manifold, aiming to stably determine a real vector field from the dynamical Dirichlet-to-Neumann map. In dimensions n >= 2, a Holder type stability estimate for the inverse problem is established, primarily relying on reduction to an equivalent problem for an electro-magnetic Schrodinger equation and the use of a Carleman estimate designed for elliptic operators.