{"title":"Optimal transport problems with the quadratic cost function","authors":"Shibing Chen, Jiakun Liu","doi":"10.1360/ssm-2023-0248","DOIUrl":null,"url":null,"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.","PeriodicalId":36277,"journal":{"name":"中国科学:数学","volume":"25 5","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"中国科学:数学","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.1360/ssm-2023-0248","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
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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