EXISTENCE OF PARTICULAR OPTIMAL TRANSPORTS FOR THEW1 WASSERSTEIN DISTANCE

) is not linear inthe variable , and that it is not even convex (it is only level-convex), whereasthe classical theory of optimal transportation usually deals with linear costs. Inparticular, our study for the existence of a transport map does not rely on the useof duality or existence of a potential (a study of these last questions is still to bedone).Bibliographie[1] G. Arronsson, M.G. Crandall and P. Juutinen, A tour of the theory of absolutelyminimizing functions, Bull. Amer. Math. Soc. (N.S.), 41, (2004), no. 4, 439{505.[2] T. Champion, L. De Pascale and P. Juutinen, The W