The flow map of the Fokker-Planck equation does not provide optimal transport

被引：3

作者：

Lavenant, Hugo ^{[1
,2
]}

Santambrogio, Filippo ^{[3
]}

机构：

[1] Bocconi Univ, Dept Decis Sci, I-20136 Milan, Italy

[2] Bocconi Univ, BIDSA, I-20136 Milan, Italy

[3] Univ Claude Bernard Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France

来源：

APPLIED MATHEMATICS LETTERS | 2022年 / 133卷

关键词：

Optimal transport; Fokker-Planck equation; Asymptotic behavior of solutions to  PDEs;

D O I：

10.1016/j.aml.2022.108225

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In Khrulkov and Oseledets (2022) the authors conjecture that, by integrating the flow of the ODE given by the Wasserstein velocity in a Fokker-Planck equation, one obtains an optimal transport map. On the other hand this result was thought to be false in Kim and Milman (2012) but no proof was provided. In this note we show that the result claimed by Khrulkov and Oseledets cannot hold. This strengthens a counterexample which was built in Tanana (2021). (c) 2022 Elsevier Ltd. All rights reserved.

引用

页数：7

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