{"title":"Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications","authors":"Fausto Ferrari, Nicolò Forcillo","doi":"10.1007/s40574-023-00393-5","DOIUrl":null,"url":null,"abstract":"In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the norm of the gradient. In particular, we show that our argument holds in the general framework of Carnot groups.","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bollettino dell'Unione Matematica Italiana","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40574-023-00393-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the norm of the gradient. In particular, we show that our argument holds in the general framework of Carnot groups.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
