{"title":"度量度量空间中拟线性奇异问题的变分极小值的不存在性","authors":"Prashanta Garain, J. Kinnunen","doi":"10.1090/proc/15417","DOIUrl":null,"url":null,"abstract":"In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincare inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces\",\"authors\":\"Prashanta Garain, J. Kinnunen\",\"doi\":\"10.1090/proc/15417\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincare inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.\",\"PeriodicalId\":8445,\"journal\":{\"name\":\"arXiv: Analysis of PDEs\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Analysis of PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/proc/15417\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/proc/15417","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces
In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincare inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.
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