Archive for Rational Mechanics and Analysis

, Volume 231, Issue 2, pp 1045–1071 | Cite as

Continuity for the Monge Mass Transfer Problem in Two Dimensions

  • Qi-Rui Li
  • Filippo SantambrogioEmail author
  • Xu-Jia Wang


In this paper, we prove the continuity of the monotone optimal mapping of the Monge mass transfer problem in two dimensions under certain conditions on the domains and the mass distributions.


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Conflict of interest

The authors declare that they have no conflict of interest.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre for Mathematics and Its ApplicationsAustralian National UniversityCanberraAustralia
  2. 2.Laboratoire de Mathématiques d’OrsayUniv. Paris-Sud, CNRS, Université Paris-SaclayOrsay cedexFrance

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