Determining The Magnetic Potential In The Fractional Magnetic Calder\'on Problem

Abstract

We determine both the magnetic potential and the electric potential from the exterior partial measurements of the Dirichlet-to-Neumann map in the fractional linear magnetic Calder\'on problem by using an integral identity. We also determine both the magnetic potential and the nonlinearity in the fractional semilinear magnetic Calder\'on problem by using a first order linearization.