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

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.