On the continuity of the total cost in the mass transport problem with   relativistic cost functions
  In this paper we consider the mass transport problem in the case of a relativistic cost; we can establish the continuity of the total cost, together with a general estimate about the directions in which the mass can actually move, under mild assumptions. These results generalize those recently obtained by J.Bertrand, A.Pratelli and M.Puel, also positively answering some of the open questions there. 
Jean Louet (CEREMADE, MOKAPLAN), Aldo Pratelli, Florian Zeisler
math.OC