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A characterization for solutions of the Monge-Kantorovich mass transport problem

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Abstract

A measure theoretical approach is presented to study the solutions of the Monge-Kantorovich optimal mass transport problems. This approach together with Kantorovich duality provide an effective tool to answer a long standing question about the support of optimal plans for the mass transport problem involving general cost functions. We also establish a criterion for the uniqueness.

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Acknowledgments

I would like to thank Professor Robert McCann for pointing out a critical issue on the statement of Theorem 1.3 in the first version of this Manuscript. I would also like to thank the reviewers for the careful reading of the manuscript and valuable comments that improved the clarity of the original manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Abbas Moameni

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  1. Abbas Moameni
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Correspondence to Abbas Moameni.

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Supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

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Moameni, A. A characterization for solutions of the Monge-Kantorovich mass transport problem. Math. Ann. 365, 1279–1304 (2016). https://doi.org/10.1007/s00208-015-1312-y

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