离散远程平均场相互作用的最优输运

IF 1.1 2区数学 Q1 MATHEMATICS

Bulletin of Mathematical Sciences Pub Date : 2018-09-19 DOI:10.1142/s1664360720500113

Jiakun Liu, G. Loeper

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引用次数: 2

摘要

我们研究了一个最优输运问题，其中，在某个中间时间，质量要么被外力加速，要么被自相互作用加速。从最优输运[X.-N.]得到了与所谓的Ma-Trudinger-Wang条件有关的相互作用势条件下的速度势、中间密度和最优输运图的规律性。妈，n·s·特鲁丁格和x·j。王，最优运输问题的势函数的正则性，[j]。配给。动力机械。书刊。177(2005)151-183。

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Optimal transport with discrete long-range mean-field interactions

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.].

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来源期刊

Bulletin of Mathematical Sciences MATHEMATICS-

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： The Bulletin of Mathematical Sciences, a peer-reviewed, open access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (up to 15 pages) containing significant results of wider interest. Most of the expository articles will be invited. The Bulletin of Mathematical Sciences is launched by King Abdulaziz University, Jeddah, Saudi Arabia.