{"title":"各向异性p→-拉普拉斯模型下全非线性方程粘度解的正则性","authors":"F. Demengel","doi":"10.3233/ASY-171433","DOIUrl":null,"url":null,"abstract":"This paper is devoted to some Lipschitz estimates between sub-and super-solutions of Fully Nonlinear equations on the model of the anisotropic ~ p-Laplacian. In particular we derive from the results enclosed that the continuous viscosity solutions for the equation ∑N 1 ∂i(∂iu| i∂iu) = f are Lipschitz continuous when supi pi < infi pi + 1, where ~ p = ∑ i piei.","PeriodicalId":8603,"journal":{"name":"Asymptot. Anal.","volume":"17 1","pages":"27-43"},"PeriodicalIF":0.0000,"publicationDate":"2017-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Regularity properties of viscosity solutions for fully nonlinear equations on the model of the anisotropic p →-Laplacian\",\"authors\":\"F. Demengel\",\"doi\":\"10.3233/ASY-171433\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is devoted to some Lipschitz estimates between sub-and super-solutions of Fully Nonlinear equations on the model of the anisotropic ~ p-Laplacian. In particular we derive from the results enclosed that the continuous viscosity solutions for the equation ∑N 1 ∂i(∂iu| i∂iu) = f are Lipschitz continuous when supi pi < infi pi + 1, where ~ p = ∑ i piei.\",\"PeriodicalId\":8603,\"journal\":{\"name\":\"Asymptot. Anal.\",\"volume\":\"17 1\",\"pages\":\"27-43\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-10-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asymptot. Anal.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3233/ASY-171433\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptot. Anal.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3233/ASY-171433","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
摘要
研究了各向异性~ p- laplace模型上的完全非线性方程的子解和超解之间的Lipschitz估计。特别地,我们从所附的结果中推导出方程∑N 1∂i(∂iu| i∂iu) = f的连续粘度解在supi pi < infi pi + 1时是Lipschitz连续的,其中~ p =∑i pii。
Regularity properties of viscosity solutions for fully nonlinear equations on the model of the anisotropic p →-Laplacian
This paper is devoted to some Lipschitz estimates between sub-and super-solutions of Fully Nonlinear equations on the model of the anisotropic ~ p-Laplacian. In particular we derive from the results enclosed that the continuous viscosity solutions for the equation ∑N 1 ∂i(∂iu| i∂iu) = f are Lipschitz continuous when supi pi < infi pi + 1, where ~ p = ∑ i piei.