Archive for Rational Mechanics and Analysis

, Volume 177, Issue 2, pp 151–183

Regularity of Potential Functions of the Optimal Transportation Problem

Article

Abstract

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.

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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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