{"title":"非线性算子的单调性控制","authors":"Michał Borowski, Iwona Chlebicka","doi":"10.1016/j.exmath.2022.07.002","DOIUrl":null,"url":null,"abstract":"<div><p>Controlling the monotonicity and growth of Leray–Lions’ operators including the <span><math><mi>p</mi></math></span>-Laplacian plays a fundamental role in the theory of existence and regularity of solutions to second order nonlinear PDEs. We collect, correct, and supply known estimates including the discussion on the constants. Moreover, we provide a comprehensive treatment of related results for operators with Orlicz growth. We pay special attention to exposition of the proofs and the use of elementary arguments.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086922000408/pdfft?md5=49850269d5e28c150251fbd05421ce5f&pid=1-s2.0-S0723086922000408-main.pdf","citationCount":"5","resultStr":"{\"title\":\"Controlling monotonicity of nonlinear operators\",\"authors\":\"Michał Borowski, Iwona Chlebicka\",\"doi\":\"10.1016/j.exmath.2022.07.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Controlling the monotonicity and growth of Leray–Lions’ operators including the <span><math><mi>p</mi></math></span>-Laplacian plays a fundamental role in the theory of existence and regularity of solutions to second order nonlinear PDEs. We collect, correct, and supply known estimates including the discussion on the constants. Moreover, we provide a comprehensive treatment of related results for operators with Orlicz growth. We pay special attention to exposition of the proofs and the use of elementary arguments.</p></div>\",\"PeriodicalId\":50458,\"journal\":{\"name\":\"Expositiones Mathematicae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0723086922000408/pdfft?md5=49850269d5e28c150251fbd05421ce5f&pid=1-s2.0-S0723086922000408-main.pdf\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Expositiones Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0723086922000408\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086922000408","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Controlling the monotonicity and growth of Leray–Lions’ operators including the -Laplacian plays a fundamental role in the theory of existence and regularity of solutions to second order nonlinear PDEs. We collect, correct, and supply known estimates including the discussion on the constants. Moreover, we provide a comprehensive treatment of related results for operators with Orlicz growth. We pay special attention to exposition of the proofs and the use of elementary arguments.
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