Rectifiability of Optimal Transportation Plans
Analysis of PDEs
2019-08-15 v1
Abstract
The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere.
Cite
@article{arxiv.1003.4556,
title = {Rectifiability of Optimal Transportation Plans},
author = {Robert J. McCann and Brendan Pass and Micah Warren},
journal= {arXiv preprint arXiv:1003.4556},
year = {2019}
}