Abstract

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\mathbb{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

Author information

Contact details are reproduced from the original publication and may be historical.

G. Carlier

Université Bordeaux 1, MAB, UMR CNRS 5466, Bordeaux, France
and: Université Bordeaux IV, GRAPE, UMR CNRS 5113, Avenue Léon Duguit, 33608, Pessac, France

Guillaume.Carlier@math.u-bordeaux.fr

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Suggested citation

G. Carlier. “On a Class of Multidimensional Optimal Transportation Problems.” Journal of Convex Analysis 10 (2003), No. 2, 517–529. https://doi.org/10.68381/jca1032

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Published by Heldermann Verlag, 2003. Rights now held by Banach Press LLC.