Rectifiability of Optimal Transportation Plans

Details Rectifiability of Optimal Transportation Plans Rectifiability of Optimal Transportation Plans

2010-03-23

arxiv.org/abs/1003.4556v1

Mathematics

Analysis of PDEs

Scientific paper

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 $C^{2}$ 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.

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