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Results tagged with optimal-transportation
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user 58975
2
votes
Accepted
Open problem 1.28: $W^{1,1}$ regularity for optimal transport map
The problem has indeed been solved by De Philippis-Figalli. The reference is:
https://link.springer.com/article/10.1007/s00222-012-0405-4
the paper linked above is a subsequent, related, development o …
- 660
8
votes
Accepted
Reference request: Wasserstein metric spaces for non linear weights/mobility?
Yes, this issue has been considered. You can start having a look at `A new class of transport distances between measures' by Dolbeault, Nazaret and Savaré (http://link.springer.com/article/10.1007%2F …
- 660
7
votes
Accepted
About the metrizability of the space of Probability measures $\mathcal{P}(S)$
I'm not really sure what Villani wrote in his monograph, but it is true that one needs to prove that the weak topology is induced by a distance, as a priori it could be another topology with the same …
- 660