Vol. 9, No. 6, 2016

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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
Abstract

We provide a different proof for the global ${C}^{1,\alpha }$ 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