2012/12/07 by Ghoussoub, Nassif, Maurey, Bernard
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1212.1680
Symmetric Monge-Kantorovich transport problems involving a cost function given by a family of vector fields were used by Ghoussoub-Moameni to establish polar decompositions of such vector fields into m-cyclically monotone maps composed with measure preserving m-involutions (m≥ 2). In this note, we relate these symmetric transport problems to the Brenier solutions of the Monge and Monge-Kantorovich problem, as well as to the Gangbo-Świȩch solutions of their multi-marginal counterparts, both of which involving quadratic cost functions.