Boundary C1,α regularity of potential functions in optimal transportation with quadratic cost

Andriyanova, Elina; Chen, Shibing

doi:10.2140/apde.2016.9.1483

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Boundary $C^{1,\alpha}$ regularity of potential functions in optimal transportation with quadratic cost

Elina Andriyanova and Shibing Chen

Vol. 9 (2016), No. 6, 1483–1496

DOI: 10.2140/apde.2016.9.1483

Abstract

We provide a different proof for the global $C^{1, α}$ regularity of potential functions in the optimal transport problem, which was originally proved by Caffarelli. Our method applies to a more general class of domains.

Keywords

optimal transport, quadratic cost, boundary regularity

Mathematical Subject Classification 2010

Primary: 35B45, 35J60, 49Q20, 35J96

Milestones

Received: 20 November 2015

Revised: 8 March 2016

Accepted: 29 April 2016

Published: 3 October 2016

Authors

Elina Andriyanova
Mathematical Science Institute The Australian National University Canberra ACT 2601 Australia

Shibing Chen
Mathematical Science Institute The Australian National University Canberra ACT 2601 Australia

Vol. 9, No. 6, 2016