Methods and Applications of Analysis
Volume 28 (2021)
Special Issue for the 60th Birthday of John Urbas: Part II
Guest editors: Neil Trudinger and Xu-Jia Wang (Australian National University)
Weak formulation of the MTW condition and convexity properties of potentials
Pages: 53 – 60
We simplify the geometric interpretation of the weak Ma–Trudinger–Wang condition for regularity in optimal transportation and provide a largely geometric proof of the global $c$-convexity of locally $c$-convex potentials when the cost function $c$ is only assumed twice differentiable.
cost function, convexity
2010 Mathematics Subject Classification
The authors’ research was partially supported by Australian Research Council Grants DP170100929, DP180100431.
Received 3 September 2020
Accepted 18 November 2020
Published 1 December 2021