{"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":"40 4","pages":"Pages 1159-1180"},"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}
引用次数: 5
Abstract
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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