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Regular version of the site

Article

The Monge-Kantorovich problem: Achievements, connections, and perspectives

Russian Mathematical Surveys. 2012. Vol. 67. No. 5. P. 785-890.
Kolesnikov A., Bogachev V.

This article gives a survey of recent research related to the Monge-Kantorovich problem. Principle results are presented on the existence of solutions and their properties both in the Monge optimal transportation problem and the Kantorovich optimal plan problem, along with results on the connections between both problems and the cases when they are equivalent. Diverse applications of these problems in non-linear analysis, probability theory, and differential geometry are discussed.