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Science China Mathematics

, Volume 62, Issue 11, pp 2057–2072 | Cite as

Global regularity of optimal mappings in non-convex domains

  • Shibing Chen
  • Jiakun Liu
  • Xu-Jia WangEmail author
Articles
  • 37 Downloads

Abstract

In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.

Keywords

Monge-Ampère equation optimal transportation global regularity 

MSC(2010)

35J96 35J25 35B65 

Notes

Acknowledgements

This work was supported by Australian Research Council (Grant Nos. FL130100118 and DP170100929).

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiChina
  2. 2.School of Mathematics and Applied StatisticsUniversity of WollongongWollongongAustralia
  3. 3.Centre for Mathematics and Its ApplicationsThe Australian National UniversityCanberraAustralia

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