Published Paper

Inserted: 29 jan 2016
Last Updated: 19 aug 2024

Journal: J. Math. Pures Appl.
Year: 2016

Abstract:

We prove some stability results concerning the smoothness of optimal transport maps with general cost functions. In particular, we show that the smoothness of optimal transport maps is an open condition with respect to the cost function and the densities. As a consequence, we obtain regularity for a large class of transport problems where the cost does not necessarily satisfy the MTW condition.

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• perturbation_1.pdf