Archive for Rational Mechanics and Analysis

, Volume 177, Issue 2, pp 151–183

Regularity of Potential Functions of the Optimal Transportation Problem

Authors

  • Xi-Nan Ma
    • Centre for Mathematics and Its ApplicationsThe Australian National University
    • Centre for Mathematics and Its ApplicationsThe Australian National University
  • Xu-Jia Wang
    • Centre for Mathematics and Its ApplicationsThe Australian National University
Article

DOI: 10.1007/s00205-005-0362-9

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

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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© Springer-Verlag Berlin Heidelberg 2005