Determining a magnetic Schroedinger operator from partial Cauchy data
  In this paper we show, in dimension n >=3, that knowledge of the Cauchy data for the Schroedinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. 
David Dos Santos Ferreira, Carlos Kenig, Johannes Sjoestrand, Gunther   Uhlmann