双非线性带权抛物型方程解的正则性

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2014-11-05 DOI:10.1090/s0077-1554-2014-00237-5

M. D. SURNACH¨EV, Boris Moiseevich Levitan

{"title":"双非线性带权抛物型方程解的正则性","authors":"M. D. SURNACH¨EV, Boris Moiseevich Levitan","doi":"10.1090/s0077-1554-2014-00237-5","DOIUrl":null,"url":null,"abstract":". We study local regularity of solutions of nonlinear parabolic equations with a double degeneracy and a weight. We impose the condition of p -admissibility on the weight; in particular this allows weights in the Muckenhoupt classes A p . We prove that solutions are locally H¨olderian without any restriction on the sign being constant. We prove a Harnack inequality for nonnegative solutions. We examine the stability of the constants as the parameters in the equation approach the linear case.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"75 1","pages":"259-280"},"PeriodicalIF":0.0000,"publicationDate":"2014-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/s0077-1554-2014-00237-5","citationCount":"10","resultStr":"{\"title\":\"Regularity of solutions of parabolic equations with a double nonlinearity and a weight\",\"authors\":\"M. D. SURNACH¨EV, Boris Moiseevich Levitan\",\"doi\":\"10.1090/s0077-1554-2014-00237-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We study local regularity of solutions of nonlinear parabolic equations with a double degeneracy and a weight. We impose the condition of p -admissibility on the weight; in particular this allows weights in the Muckenhoupt classes A p . We prove that solutions are locally H¨olderian without any restriction on the sign being constant. We prove a Harnack inequality for nonnegative solutions. We examine the stability of the constants as the parameters in the equation approach the linear case.\",\"PeriodicalId\":37924,\"journal\":{\"name\":\"Transactions of the Moscow Mathematical Society\",\"volume\":\"75 1\",\"pages\":\"259-280\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/s0077-1554-2014-00237-5\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the Moscow Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/s0077-1554-2014-00237-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Moscow Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/s0077-1554-2014-00237-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 10

摘要

．研究了一类具有重退化和权的非线性抛物型方程解的局部正则性。我们对权值施加p -可容许性条件;特别是，这允许在Muckenhoupt类A p中的权重。我们证明了解是局部H′olderian的，不受符号为常数的限制。我们证明了一个非负解的哈纳克不等式。在接近线性的情况下，我们检验了常数作为参数的稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Regularity of solutions of parabolic equations with a double nonlinearity and a weight

. We study local regularity of solutions of nonlinear parabolic equations with a double degeneracy and a weight. We impose the condition of p -admissibility on the weight; in particular this allows weights in the Muckenhoupt classes A p . We prove that solutions are locally H¨olderian without any restriction on the sign being constant. We prove a Harnack inequality for nonnegative solutions. We examine the stability of the constants as the parameters in the equation approach the linear case.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

自引率

0.00%

发文量

期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.