超立方体间最优映射的正则性

IF 2.1 2区数学 Q1 MATHEMATICS

Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI:10.1515/ans-2023-0087

Shibing Chen, Jiakun Liu, Xu-Jia Wang

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引用次数: 0

摘要

摘要本文建立了{R n }{}{{\mathbb{R}}}{ ^n中n≥3n时超立方体间最优运输势函数}的全局 3， α C^3, {\alpha}正则性{}\ge 3。当n=2 n=2时，Jhaveri证明了结果。{由于Jhaveri研究中的一个反例，}c3， α {C, \alpha正则性也是最优的。}

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Regularity of optimal mapping between hypercubes

Abstract In this note, we establish the global C 3 , α {C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in R n {{\mathbb{R}}}^{n} for n ≥ 3 n\ge 3 . When n = 2 n=2 , the result was proved by Jhaveri. The C 3 , α {C}^{3,\alpha } regularity is also optimal due to a counterexample in the study by Jhaveri.

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来源期刊

Advanced Nonlinear Studies 数学-数学

CiteScore

3.00

自引率

5.60%

发文量

审稿时长

12 months

期刊介绍： Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.