{"title":"Some useful tools in the study of nonlinear elliptic problems","authors":"Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu","doi":"10.1016/j.exmath.2024.125616","DOIUrl":null,"url":null,"abstract":"<div><p>This paper gives an overview of some basic aspects concerning the qualitative analysis of nonlinear, nonhomogeneous elliptic problems. We are concerned with two classes of elliptic equations with Dirichlet boundary condition. The first problem is driven by a general nonhomogeneous differential operator, which includes several usual operators (such as the <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-Laplace operator introduced by P. Marcellini). Next, we focus on differential operators with unbalanced growth in the nonautonomous case. Our analysis will point out some relevant differences between balanced and unbalanced growth problems. The presentation is done in the context of Dirichlet problems but a similar analysis can be developed for other boundary conditions, such as Neumann or Robin.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 6","pages":"Article 125616"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000835/pdfft?md5=7c5aee29b49c6102b8de52d2790f9ff3&pid=1-s2.0-S0723086924000835-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086924000835","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: 0
Abstract
This paper gives an overview of some basic aspects concerning the qualitative analysis of nonlinear, nonhomogeneous elliptic problems. We are concerned with two classes of elliptic equations with Dirichlet boundary condition. The first problem is driven by a general nonhomogeneous differential operator, which includes several usual operators (such as the -Laplace operator introduced by P. Marcellini). Next, we focus on differential operators with unbalanced growth in the nonautonomous case. Our analysis will point out some relevant differences between balanced and unbalanced growth problems. The presentation is done in the context of Dirichlet problems but a similar analysis can be developed for other boundary conditions, such as Neumann or Robin.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
