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Journal of Convex Analysis 10 (2003), No. 2, 517--529
Copyright Heldermann Verlag 2003

On a Class of Multidimensional Optimal Transportation Problems

G. Carlier
Université Bordeaux 1, MAB, UMR CNRS 5466, Bordeaux, France, Guillaume.Carlier@math.u-bordeaux.fr

We prove existence, uniqueness, duality results and give a characterization of optimal measure-preserving maps for a class of optimal transportation problems with several marginals with compact support in R under the requirement that the cost function satisfies a so-called monotonicity of order 2 condition. Explicit formulas for the minimizers are given and links with some rearrangement inequalities are sketched.

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