Verena Bogelein, F. Duzaar, Naian Liao, Leah Schatzler
{"title":"关于一个双非线性方程有符号解的Hölder正则性。第二部分","authors":"Verena Bogelein, F. Duzaar, Naian Liao, Leah Schatzler","doi":"10.4171/rmi/1342","DOIUrl":null,"url":null,"abstract":"We demonstrate two proofs for the local H\\\"older continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \\[ \\partial_t\\big(|u|^{q-1}u\\big)-\\Delta_p u=0,\\quad p>2,\\quad 0<q<p-1. \\] The first proof takes advantage of the expansion of positivity for the degenerate, parabolic $p$-Laplacian, thus simplifying the argument; whereas the other proof relies solely on the energy estimates for the doubly nonlinear parabolic equations. After proper adaptions of the interior arguments, we also obtain the boundary regularity for initial-boundary value problems of Dirichlet type and Neumann type.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II\",\"authors\":\"Verena Bogelein, F. Duzaar, Naian Liao, Leah Schatzler\",\"doi\":\"10.4171/rmi/1342\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We demonstrate two proofs for the local H\\\\\\\"older continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \\\\[ \\\\partial_t\\\\big(|u|^{q-1}u\\\\big)-\\\\Delta_p u=0,\\\\quad p>2,\\\\quad 0<q<p-1. \\\\] The first proof takes advantage of the expansion of positivity for the degenerate, parabolic $p$-Laplacian, thus simplifying the argument; whereas the other proof relies solely on the energy estimates for the doubly nonlinear parabolic equations. After proper adaptions of the interior arguments, we also obtain the boundary regularity for initial-boundary value problems of Dirichlet type and Neumann type.\",\"PeriodicalId\":49604,\"journal\":{\"name\":\"Revista Matematica Iberoamericana\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2021-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Matematica Iberoamericana\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/rmi/1342\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Matematica Iberoamericana","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/rmi/1342","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II
We demonstrate two proofs for the local H\"older continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\big(|u|^{q-1}u\big)-\Delta_p u=0,\quad p>2,\quad 0
期刊介绍：
Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.
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