[1]陈 平.传输密度的Lp,q估计[J].南京师大学报(自然科学版),2022,45(01):8-11.[doi:10.3969/j.issn.1001-4616.2022.01.002]
　Chen Ping.Lp,q Estimation of a Transport Density[J].Journal of Nanjing Normal University(Natural Science Edition),2022,45(01):8-11.[doi:10.3969/j.issn.1001-4616.2022.01.002]
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传输密度的Lp,q估计()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第45卷
期数:
2022年01期
页码:
8-11
栏目:
·数学·
出版日期:
2022-03-15

文章信息/Info

Title:
Lp,q Estimation of a Transport Density
文章编号:
1001-4616(2022)01-0008-04
作者:
陈 平
(江苏第二师范学院数学与信息技术学院,江苏 南京 210013)
Author(s):
Chen Ping
(School of Mathematics and Information Technology,Jiangsu Second Normal University,Nanjing 210013,China)
关键词:
Lp; q估计; 传输密度; 位移内插
Keywords:
Lp; q estimate; transport density; displacement interpolations
分类号:
O186.14
DOI:
10.3969/j.issn.1001-4616.2022.01.002
文献标志码:
A
摘要:
研究了与两个概率测度μ和v之间的最优计划γ有关的传输密度σγ的绝对连续性和Lp,q可和性. 更确切地说,如果μ∈Lp,q,其中1≤p<+∞,1≤q<+∞以及v的支撑集合为有限点集,则有σγ∈Lp,q. 本文的证明主要利用经由位移内插μt给出了σγ的等价定义公式,σγ与μt的关系不等式,以及对位移内插μt进行的Lp,q估计.
Abstract:
The paper presents the absolute continuity and Lp,q summability of a transport density σγ associated to an optimal transport plan γ between two probability measures μ and v. More precisely,σγ∈Lp,q holds if μ∈Lp,q where 1≤p<+∞,1≤q<+∞ and v has a finite support set. The main methods we used include the equivalent redefinition of σγ by displacement interpolations μt,the relationship inequality between σγ and μt,and the Lp,q estimation of such interpolations μt.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2021-07-12.
基金项目:国家自然科学基金青年项目(11601193)、国家自然科学基金面上项目(12071219).
通讯作者:陈平,博士,副教授,研究方向:最优运输,偏微分方程,几何分析. E-mail:chenping200507@126.com
更新日期/Last Update: 1900-01-01