Optimal transport problems with the quadratic cost function

Q3 Mathematics

中国科学:数学 Pub Date : 2024-01-01 DOI:10.1360/ssm-2023-0248

Shibing Chen, Jiakun Liu

引用次数: 0

Abstract

The squared distance function is one of the most important cost functions in optimal transport problems, and it has signi(cid:12)cant applications in many (cid:12)elds. In this paper, we brie(cid:13)y introduce the optimal transport problems under this cost function, including the existence, regularity, and partial regularity of solutions, as well as related free boundary problems.

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具有二次成本函数的最优运输问题

平方距离函数是最优运输问题中最重要的代价函数之一，它在许多（cid:12）领域都有重要应用。本文简要介绍了该代价函数下的最优运输问题，包括解的存在性、正则性和部分正则性，以及相关的自由边界问题。

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

中国科学:数学 Mathematics-Mathematics (all)

CiteScore

1.20

自引率

0.00%

发文量

6663

期刊介绍： Scientia Sinica Mathematica (in Chinese) and (in English) are comprehensive academic journals in mathematics under the auspices of the Chinese Academy of Sciences and co-sponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China. It mainly reports the important research results in basic mathematics, applied mathematics, computational mathematics and scientific engineering computation, and probability statistics. Published by Science China. Monthly. Chinese edition: online edition published on the 1st of every month, print edition published on the 20th of every month. English: The online version is published on the 20th of the month preceding the month in which the print version is published, and the print version is published on the 1st of the month. The Chinese version of Scientia Sinica Mathematica is indexed in China Science Citation Database, China Academic Journal Network, Chinese Science and Technology Journal Database, China Science Literature Database, China Digital Journals, Chinese Core Journals, Scopus, etc. The English version is an SCI journal.