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Results tagged with optimal-transportation
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user 137743
3
votes
1
answer
290
views
Open problem 1.28: $W^{1,1}$ regularity for optimal transport map
While I don't work on the regularity theory for the optimal transport map, I was curious about the open problem 1.28 listed in Ambrosio and Gigli's User's guide: the problem to determine whether we ha …
- 183
1
vote
0
answers
36
views
Sufficient condition for an $n$-tuple to be a convex conjugate
We say $(f_1,f_2,\dotsc,f_N)$ is a convex conjugate if for any $i=1,2,\dotsc,N$ and any $x_i\in\Bbb R^d$, we have:
$$f_i(x_i)=\sup\left\{\sum_{k=1}^{N}\sum_{j=k+1}^N x_k x_j - \sum_{j=1,j\neq i}^N f_j …
- 183
0
votes
The uniqueness of Barycenters in the Wasserstein space
I agree with the answer by @Gabriel Clara in principle. However I feel it is not complete clear in their proof. They basically wanted to rely on the uniqueness from Brenier map between one marginal $\ …
- 183