Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere

Details Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere

2011-01-26

arxiv.org/abs/1101.5146v3

Mathematics

Analysis of PDEs

15 pages. Added gradient estimate depending on Wasserstein distance (see section 5)

Scientific paper

We give sufficient conditions on initial and target measures supported on the
sphere $\S^n$ to ensure the solution to the optimal transport problem with the
cost $|x-y|^2/2$ is a diffeomorphism.

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