An inverse boundary value problem for Schrödinger operators with vector potentials

We consider the Schrödinger operator for a magnetic potential A → A and an electric potential q q, which are supported in a bounded domain in R n {Rⁿ} with n ≥ 3 n 3. We prove that knowledge of the Dirichlet to Neumann map associated to the Schrödinger operator determines the magnetic field rot ⁡ (A →) rot (A) and the electric potential q q simultaneously, provided rot ⁡ (A →) rot (A) is small in the L ∞ L^ topology.