A Computational Fluid Me hani s solution to the

A Computational Fluid Me hani s solution to the Monge-Kantorovi h mass transfer problem. Jean-David Benamou Yann Brenier y July 9, 2001 Abstra t The L 2 Monge-Kantorovi h mass transfer problem [31? is reset in a Fluid Me hani s framework and numeri ally solved by an augmented La- grangian method. 1 Introdu tion The rst mass transfer problem was onsidered by Monge in 1781 in his \memoire sur la theorie des deblais et des remblais, a Civil Engineering problem where par els of materials have to be displa ed from one site to another one with minimal transportation ost. A modern treatment of this problem has been initiated by Kantorovi h in 1942 ( f. [23? for the english version), leading to the so- alled Monge-Kantorovi h problem whi h has re eived a onsiderable interest in the re ent years, with a wide range of potential appli ations and extensions. A re ent omprehensive review an be found in the new books by Ra hev and Rus hendorf [31?, the le ture notes by Evans [19? and the review paper by M Cann and Gangbo [21?. The framework of the Monge-Kantorovi h problem is as follows. Two density fun tions 0 (x) 0 and T (x) 0 of x 2 R d , that we assume to be bounded with total mass one Z

• fun tions


• ee tive


• tive proof


• problem


• monge-ampere equation


• lagrangian method


• problem has


• standard boundary


• alled alg2


• numeri al