非线性算子的单调性控制

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2022-12-01 DOI:10.1016/j.exmath.2022.07.002

Michał Borowski, Iwona Chlebicka

{"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":"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":"{\"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}","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

摘要

在二阶非线性偏微分方程解的存在性和正则性理论中，控制包括p-拉普拉斯算子在内的Leray-Lions算子的单调性和生长性具有重要意义。我们收集、修正和提供已知的估计，包括对常数的讨论。此外，我们还为Orlicz生长的操作者提供了相关结果的综合处理。我们特别注意证明的阐述和初等论证的使用。

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

Controlling monotonicity of nonlinear operators

Controlling the monotonicity and growth of Leray–Lions’ operators including the $p$ -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.

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

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

期刊介绍： Our aim is to publish papers of interest to a wide mathematical audience. Our main interest is in expository articles that make high-level research results more widely accessible. In general, material submitted should be at least at the graduate level.Main articles must be written in such a way that a graduate-level research student interested in the topic of the paper can read them profitably. When the topic is quite specialized, or the main focus is a narrow research result, the paper is probably not appropriate for this journal. Most original research articles are not suitable for this journal, unless they have particularly broad appeal.Mathematical notes can be more focused than main articles. These should not simply be short research articles, but should address a mathematical question with reasonably broad appeal. Elementary solutions of elementary problems are typically not appropriate. Neither are overly technical papers, which should best be submitted to a specialized research journal.Clarity of exposition, accuracy of details and the relevance and interest of the subject matter will be the decisive factors in our acceptance of an article for publication. Submitted papers are subject to a quick overview before entering into a more detailed review process. All published papers have been refereed.