C 2 , α $C^{2,\alpha }$ regularity of free boundaries in optimal transportation

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-09-07 DOI:10.1002/cpa.22151

Shibing Chen, Jiakun Liu, Xu-Jia Wang

引用次数: 0

Abstract

The regularity of the free boundary in optimal transportation is equivalent to that of the potential function along the free boundary. By establishing new geometric estimates of the free boundary and studying the second boundary value problem of the Monge-Ampère equation, we obtain the $C^{2, α}$ regularity of the potential function as well as that of the free boundary, thereby resolve an open problem raised by Caffarelli and McCann.

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最优运输中自由边界的C2，α$C^{2，\alpha}$正则性

最优输运中自由边界的规律性等同于沿自由边界的势函数的规律性。通过建立新的自由边界几何估计和研究Monge - ampetrre方程的第二边值问题，我们得到了势函数和自由边界的正则性，从而解决了Caffarelli和McCann提出的一个开放性问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.