On the Monge mass transfer problem
نویسندگان
چکیده
The Monge mass transfer problem, as proposed by Monge in 1781, is to move points from one mass distribution to another so that a cost functional is minimized among all measure preserving maps. The existence of an optimal mapping was proved by Sudakov in 1979, using probability theory. A proof based on partial differential equations was recently found by Evans andGangbo. In this paperwegive amore elementary and shorter proof by constructing an optimal mapping directly from the potential functions of Monge and Kantorovich. Mathematics Subject Classification (1991):49Q20, 49J10
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