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Optimal transport with discrete long-range mean-field interactions

Jiakun Liu

School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia

E-mail Address: jiakunl@uow.edu.au

Corresponding author.

This work was partially supported by the Australian Research Council DP170100929 and DP200101084.

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and

Grégoire Loeper

School of Mathematical Sciences, Monash University, Melbourne, VIC 3800, Australia

E-mail Address: gregoire.loeper@monash.edu

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https://doi.org/10.1142/S1664360720500113Cited by:0 (Source: Crossref)

Abstract

We study an optimal transport problem where, at some intermediate time, the mass is either accelerated by an external force field or self-interacting. We obtain the regularity of the velocity potential, intermediate density, and optimal transport map, under the conditions on the interaction potential that are related to the so-called Ma–Trudinger–Wang condition from optimal transport [X.-N. Ma, N. S. Trudinger and X.-J. Wang, Regularity of potential functions of the optimal transportation problems, Arch. Ration. Mech. Anal.177 (2005) 151–183.].

Communicated by Neil Trudinger

Keywords:

AMSC: 35J96, 37J50

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Vol. 10, No. 02

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History

Received 17 December 2019

Revised 24 February 2020

Accepted 9 March 2020

Published: 12 May 2020

Information

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Optimal transport with discrete long-range mean-field interactions

Abstract

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