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arXiv:2410.06230 [math.AP]AbstractReferencesReviewsResources

Pointwise Schauder estimates for optimal transport maps of rough densities

Arghya Rakshit

Published 2024-10-08Version 1

We prove a pointwise $C^{2,\,\alpha}$ estimate for the potential of the optimal transport map in the case that the densities are only close to a constant in a certain $L^p$ sense. To do so we use the variational approach recently developed by Goldman-Otto[ Ann. Sci. \'Ec. Norm. Sup\'er.(2020)].

Comments: 26 pages, 3 figures, comments are welcome
Categories: math.AP
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