Abstract.
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 and Gangbo. In this paper we give a more elementary and shorter proof by constructing an optimal mapping directly from the potential functions of Monge and Kantorovich.
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Received May 23, 2000 / Accepted June 12, 2000 / Published online November 9, 2000
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Trudinger, N., Wang, XJ. On the Monge mass transfer problem. Calc Var 13, 19–31 (2001). https://doi.org/10.1007/PL00009922
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DOI: https://doi.org/10.1007/PL00009922