{"title":"紧黎曼流形之间p调和映射的热方程","authors":"Ali Fardoun, Rachid Regbaoui","doi":"10.1016/S0764-4442(01)02176-0","DOIUrl":null,"url":null,"abstract":"<div><p>Let (<em>M</em><sup><em>m</em></sup>,<em>g</em>) and (<em>N</em><sup><em>n</em></sup>,<em>h</em>) (<em>m</em>⩾2) be two compact Riemannian manifolds without boundary. When Riem<sub><em>N</em></sub>⩽0, we show the global existence of a weak solution of the heat equation for <em>p</em>-harmonic maps (<em>p</em>>1) and the convergence of this solution at infinity to a regular weakly <em>p</em>-harmonic map; so generalizing the result of Eells–Sampson for harmonic maps to the case that <em>p</em>>1.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 11","pages":"Pages 979-984"},"PeriodicalIF":0.0000,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02176-0","citationCount":"0","resultStr":"{\"title\":\"Équation de la chaleur pour les applications p-harmoniques entre variétés riemanniennes compactes\",\"authors\":\"Ali Fardoun, Rachid Regbaoui\",\"doi\":\"10.1016/S0764-4442(01)02176-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let (<em>M</em><sup><em>m</em></sup>,<em>g</em>) and (<em>N</em><sup><em>n</em></sup>,<em>h</em>) (<em>m</em>⩾2) be two compact Riemannian manifolds without boundary. When Riem<sub><em>N</em></sub>⩽0, we show the global existence of a weak solution of the heat equation for <em>p</em>-harmonic maps (<em>p</em>>1) and the convergence of this solution at infinity to a regular weakly <em>p</em>-harmonic map; so generalizing the result of Eells–Sampson for harmonic maps to the case that <em>p</em>>1.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 11\",\"pages\":\"Pages 979-984\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02176-0\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021760\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021760","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Équation de la chaleur pour les applications p-harmoniques entre variétés riemanniennes compactes
Let (Mm,g) and (Nn,h) (m⩾2) be two compact Riemannian manifolds without boundary. When RiemN⩽0, we show the global existence of a weak solution of the heat equation for p-harmonic maps (p>1) and the convergence of this solution at infinity to a regular weakly p-harmonic map; so generalizing the result of Eells–Sampson for harmonic maps to the case that p>1.
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