{"title":"拟线性椭圆算子可容许函数的Kato不等式","authors":"Xiaojing Liu, T. Horiuchi","doi":"10.5036/MJIU.51.49","DOIUrl":null,"url":null,"abstract":"Let 1 < p < 1 and let Ω be a bounded domain of R N ( N (cid:21) 1). In this paper, we consider a class of second order quasilinear elliptic operators A in Ω including the p -Laplace operator ∆ p . First we establish various type of Kato’s inequalities for A when A u is a Radon measure. Then we prove the inverse maximum principle and describe the strong maximum principle. For this purpose it is crucial to introduce a notion of admissible class for the operator A and use it effectively. y","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"79 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Kato's inequalities for admissible functions to quasilinear elliptic operators A\",\"authors\":\"Xiaojing Liu, T. Horiuchi\",\"doi\":\"10.5036/MJIU.51.49\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let 1 < p < 1 and let Ω be a bounded domain of R N ( N (cid:21) 1). In this paper, we consider a class of second order quasilinear elliptic operators A in Ω including the p -Laplace operator ∆ p . First we establish various type of Kato’s inequalities for A when A u is a Radon measure. Then we prove the inverse maximum principle and describe the strong maximum principle. For this purpose it is crucial to introduce a notion of admissible class for the operator A and use it effectively. y\",\"PeriodicalId\":18362,\"journal\":{\"name\":\"Mathematical Journal of Ibaraki University\",\"volume\":\"79 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Journal of Ibaraki University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/MJIU.51.49\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Journal of Ibaraki University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/MJIU.51.49","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Kato's inequalities for admissible functions to quasilinear elliptic operators A
Let 1 < p < 1 and let Ω be a bounded domain of R N ( N (cid:21) 1). In this paper, we consider a class of second order quasilinear elliptic operators A in Ω including the p -Laplace operator ∆ p . First we establish various type of Kato’s inequalities for A when A u is a Radon measure. Then we prove the inverse maximum principle and describe the strong maximum principle. For this purpose it is crucial to introduce a notion of admissible class for the operator A and use it effectively. y
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