{"title":"关于全非线性Alt-Phillips方程","authors":"Yijing Wu, Hui Yu","doi":"10.1093/IMRN/RNAA359","DOIUrl":null,"url":null,"abstract":"For a parameter $\\gamma\\in(1,2)$, we study the fully nonlinear version of the Alt-Phillips equation, $F(D^2u)=u^{\\gamma-1}$, for $u\\ge 0.$ We establish the optimal regularity of the solution, as well as the $C^1$ regularity of the regular part of the free boundary.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the Fully Nonlinear Alt–Phillips Equation\",\"authors\":\"Yijing Wu, Hui Yu\",\"doi\":\"10.1093/IMRN/RNAA359\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a parameter $\\\\gamma\\\\in(1,2)$, we study the fully nonlinear version of the Alt-Phillips equation, $F(D^2u)=u^{\\\\gamma-1}$, for $u\\\\ge 0.$ We establish the optimal regularity of the solution, as well as the $C^1$ regularity of the regular part of the free boundary.\",\"PeriodicalId\":8445,\"journal\":{\"name\":\"arXiv: Analysis of PDEs\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Analysis of PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/IMRN/RNAA359\",\"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/10.1093/IMRN/RNAA359","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
For a parameter $\gamma\in(1,2)$, we study the fully nonlinear version of the Alt-Phillips equation, $F(D^2u)=u^{\gamma-1}$, for $u\ge 0.$ We establish the optimal regularity of the solution, as well as the $C^1$ regularity of the regular part of the free boundary.
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