Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential

Abstract

We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in \({\mathbb{R}^n}\) , \({n \geq 3}\) , for the magnetic Schrodinger operator with L∞ magnetic and electric potentials, determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schrodinger operator with a gain of two derivatives.