A partial data inverse problem for the electro-magnetic wave equation and application to the related Borg–Levinson theorem

Abstract

Abstract In this article we study the stability in an inverse problem of recovering the magnetic field and the electric potential in a bounded smooth domain from boundary observation of the corresponding wave equation. We prove that the knowledge of the partial Dirichlet-to-Neumann map measured on arbitrary subset of the boundary determines the electric potential and the magnetic field. Next, we apply this result to prove the uniqueness for the multidimensional Borg–Levinson theorem for the electro-magnetic potential from partial data.