Adv. Math. Econ. Volume 6, pp.85-122 (2004)

Optimal solutions of the Monge problem

Vladimir L. Levin
Central Economics and Mathematics Institute of Russian Academy of Sciences, 47 Nakhimovskii Prospect, 117418 Moscow, Russia
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We obtain optimality conditions for Monge solutions of the Monge---Kantorovich problem with a smooth cost function. Also we give explicit solutions to Monge problems and to Monge---Kantorovich problems for several natural classes of cost functions.
Key Words:
Borel measure, marginal measure, measure preserving map, Monge problem, Monge--Kantorovich problem.