A characterization for solutions of the Monge-Kantorovich mass transport   problem
  A measure theoretical approach is presented to study the Monge-Kantorovich optimal mass transport problem. This approach together with Kantorovich duality provide an effective tool to answer a long standing question about the support of optimal plans for the mass transport problem involving general cost functions. We also establish a criterion for the uniqueness. 
Abbas Moameni
math.AP