{"title":"塞格雷定理。微分几何中一个结果的解析证明","authors":"Karl K. Brustad","doi":"10.4310/ajm.2021.v25.n3.a1","DOIUrl":null,"url":null,"abstract":"We present an analytic approach on how to solve the problem $|\\nabla u|=f(u)$, $\\Delta u = g(u)$, in connected domains $\\Omega\\subseteq\\mathbb{R}^n$.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2020-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Segre’s theorem. An analytic proof of a result in differential geometry\",\"authors\":\"Karl K. Brustad\",\"doi\":\"10.4310/ajm.2021.v25.n3.a1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an analytic approach on how to solve the problem $|\\\\nabla u|=f(u)$, $\\\\Delta u = g(u)$, in connected domains $\\\\Omega\\\\subseteq\\\\mathbb{R}^n$.\",\"PeriodicalId\":55452,\"journal\":{\"name\":\"Asian Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-02-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/ajm.2021.v25.n3.a1\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/ajm.2021.v25.n3.a1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
摘要
我们提出了一种解析方法来解决连接域$\Omega\subseteq\mathbb{R}^n$中的问题$|\nabla u|=f(u)$, $\Delta u = g(u)$。