A local uniqueness theorem for the fractional Schrödinger equation on closed Riemannian manifolds

Abstract

We investigate that a potential $V$ in the fractional Schrödinger equation $((-{\Delta }_g{)}^s+V)u=f$ can be recovered locally by using the local source-to-solution map on smooth connected closed Riemannian manifolds. To achieve this goal, we derive a related new Runge approximation property.

6 pages