{"title":"具有二次成本函数的最优运输问题","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":"{\"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}","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}
Optimal transport problems with the quadratic cost function
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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