[1]陈 平.Heisenberg群上内插的L∞范数估计[J].南京师范大学学报(自然科学版),2020,43(02):6-9.[doi:10.3969/j.issn.1001-4616.2020.02.002]
　Chen Ping.L∞ Norm Estimation of Interpolations on the Heisenberg Group[J].Journal of Nanjing Normal University(Natural Science Edition),2020,43(02):6-9.[doi:10.3969/j.issn.1001-4616.2020.02.002]
点击复制

Heisenberg群上内插的L∞范数估计()
分享到：

《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第43卷
期数:
2020年02期
页码:
6-9
栏目:
·数学·
出版日期:
2020-05-30

文章信息/Info

Title:
L ∞ Norm Estimation of Interpolations on the Heisenberg Group
文章编号:
1001-4616(2020)02-0006-04
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:
Heisenberg群; 内插; L∞范数估计
Keywords:
Heisenberg group; interpolation; L∞ norm estimation
DOI:
10.3969/j.issn.1001-4616.2020.02.002
文献标志码:
A
摘要:
本文研究了Heisenberg群(Hn,d,L2n+1)上费用函数为(d(x,y))时最优计划γ的内插μt. 其中为严格凸函数.内插的本质就是一种测度. 我们证明了该内插μt关于Lebsegue测度L2n+1是绝对连续的,同时也对μt的L∞范数进行了估计. 此外,利用这一估计结果,我们还对Heisenberg群上的变分逼近问题解的内插(etS)#γε进行了估计. 本文的证明主要利用Heisenberg群上的L2n+1测度收缩性质以及最优运输理论中的循环单调性以及的严格凸性.
Abstract:
In this paper,we discuss the interpolation μt of optimal transport plan γ in the Heisenberg group(Hn,d,L2n+1)with the cost function (d(x,y))where is a strictly convex function. An interpolation is actually a kind of measure. We show that the interpolation μt is absolutely continuous with respect to the Lebsegue measure L2n+1. We also give a L∞ norm estimation on μt. Furthermore,as a corollary of the above estimation result,we also estimate the interpolation(etS)#γε of solutions of the variational approximation problem in the Heisenberg group. The main methods we used include the L2n+1 measure contraction property of the Heisenberg group,the cyclically monotonicity in the optimal transport theory and the strictly convexity of .

参考文献/References:

[1] SANTAMBROGIO F. Absolute continuity and summability of optimal transport densities:simpler proofs and new estimates[J]. Calculus of variations and partial differential equations,2009,36(3):343-354.
[2]CHAMPION T,PASCALE L D. The monge’s problem in Rd[J]. Duke mathematical journal,2011,157:551-572.
[3]陈平. Heisenberg群上最优计划的分类[J]. 江苏第二师范学院学报(自然科学版),2016,32(12):11-14.
[4]VILLANI C. Topics in optiral transportation[M]. Providence:American Mathematical Society,2003.
[5]VILLANI C. Optimal transport:old and new[M]. New York:Springer Science and Business Media,2008.
[6]陈平. 几个最优映射存在唯一性定理的统一证明[J]. 南京师大学报(自然科学版),2015,38(4):82-85.
[7]DE PASCALE L,RIGOT S. Monge’s transport problem in the Heisenberg group[J]. Advances in calculus of variations,2011,4(2):195-227.
[8]JUILLET N. Geometric inequalities and generalized ricci bounds in the heisenberg group[J]. International mathematics research notices,2009,13:2347-2373.

相似文献/References:

[1]朱旭东,张爱良,陈殿勇,等.一种基于高效率智能型600W D类音频功率放大器设计的防火报警系统[J].南京师范大学学报(自然科学版),2016,39(04):0.[doi:10.3969/j.issn.1001-4616.2016.04.020]
　Zhu Xudong,Zhang Ailiang,Chen Dianyong,et al.A Fire Alarm System Based on High-Efficiency and SmartClass-D Audio Power Amplifier of 600W[J].Journal of Nanjing Normal University(Natural Science Edition),2016,39(02):0.[doi:10.3969/j.issn.1001-4616.2016.04.020]

备注/Memo

备注/Memo:
收稿日期:2019-04-25.
基金项目:国家自然科学基金青年项目(11601193)、2017年度江苏省高校“青蓝工程”优秀青年骨干教师培养对象计划项目、江苏省高校优秀中青年教师和校长境外研修项目.
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: 2020-05-15