{"title":"Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain","authors":"","doi":"10.1134/s0040577924010082","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p> We consider a second-order quasilinear elliptic equation with an integrable right-hand side. We formulate constraints on the structure of the equation in terms of a generalized <span> <span>\\(N\\)</span> </span>-function. We prove the existence of an entropic solution of the Dirichlet problem in nonreflexive Musielak–Orlicz–Sobolev spaces in an arbitrary unbounded strictly Lipschitz domain. </p> </span>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0040577924010082","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a second-order quasilinear elliptic equation with an integrable right-hand side. We formulate constraints on the structure of the equation in terms of a generalized \(N\)-function. We prove the existence of an entropic solution of the Dirichlet problem in nonreflexive Musielak–Orlicz–Sobolev spaces in an arbitrary unbounded strictly Lipschitz domain.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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