Archive for Rational Mechanics and Analysis

, Volume 177, Issue 2, pp 151–183

Regularity of Potential Functions of the Optimal Transportation Problem


DOI: 10.1007/s00205-005-0362-9

Cite this article as:
Ma, XN., Trudinger, N. & Wang, XJ. Arch. Rational Mech. Anal. (2005) 177: 151. doi:10.1007/s00205-005-0362-9


The potential function of the optimal transportation problem satisfies a partial differential equation of Monge-Ampère type. In this paper we introduce the notion of a generalized solution, and prove the existence and uniqueness of generalized solutions of the problem. We also prove the solution is smooth under certain structural conditions on the cost function.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Centre for Mathematics and Its ApplicationsThe Australian National UniversityCanberraAustralia

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