We consider the L∞- optimal mass transportation problem minΠ(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.
L∞-optimal transport for a class of strictly quasiconvex cost functions / Brizzi C.; De Pascale L.; Kausamo A.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 527:(2023), pp. 127331.1-127331.18. [10.1016/j.jmaa.2023.127331]
L∞-optimal transport for a class of strictly quasiconvex cost functions
Brizzi C.;De Pascale L.
;Kausamo A.
2023
Abstract
We consider the L∞- optimal mass transportation problem minΠ(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.
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