L∞-optimal transport for a class of strictly quasiconvex cost functions

We consider the L∞- optimal mass transportation problemminΠ(μ,ν)⁡γ−ess supc(x,y), for a new class of costs c(x,y) for which we introduce a tentative notion of twist condition. In particular we study the conditions under which the ∞-monotone transport plans are induced by a transportation map. We als...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2023-11, Vol.527 (1), p.127331, Article 127331
Main Authors: Brizzi, Camilla, De Pascale, Luigi, Kausamo, Anna
Format: Article
Language:English
Subjects:
[formula omitted]-optimal transport
Monge Kantorovich problem
Optimal transport problem
Wasserstein distances
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Summary:We consider the L∞- optimal mass transportation problemminΠ(μ,ν)⁡γ−ess supc(x,y), for a new class of costs c(x,y) for which we introduce a tentative notion of twist condition. In particular we study the conditions under which the ∞-monotone transport plans are induced by a transportation map. We also state a uniqueness result for infinitely cyclically monotone Monge minimizers that corresponds to this class of cost functions. We compare the results to previous works.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127331