Adv. Math. Econ. 6, 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 (email: vllevin@mail.ru)

Received: April 4, 2003 Revised: May 21, 2003 JEL classification: C65 Mathematical Subject Classification (2000): 49Q20, 28A35 Summary. 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.