{"title":"Multidimensional Zaremba problem for the \\(p(\\,\\cdot\\,)\\)-Laplace equation. A Boyarsky–Meyers estimate","authors":"Yu. A. Alkhutov, G. A. Chechkin","doi":"10.1134/S004057792401001X","DOIUrl":null,"url":null,"abstract":"<p> We prove the higher integrability of the gradient of solutions of the Zaremba problem in a bounded strongly Lipschitz domain for an inhomogeneous <span>\\(p(\\,\\cdot\\,)\\)</span>-Laplace equation with a variable exponent <span>\\(p\\)</span> having a logarithmic continuity modulus. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"218 1","pages":"1 - 18"},"PeriodicalIF":1.1000,"publicationDate":"2024-02-01","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://link.springer.com/article/10.1134/S004057792401001X","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 prove the higher integrability of the gradient of solutions of the Zaremba problem in a bounded strongly Lipschitz domain for an inhomogeneous \(p(\,\cdot\,)\)-Laplace equation with a variable exponent \(p\) having a logarithmic continuity modulus.
Abstract We prove the higher integrability of solutions of Zaremba problem in a bounded strongly Lipschitz domain for an inhomogeneous \(p(\,\cdot\,)\)-Laplace equation with a variable exponent \(p\) having a logarithmic continuity modulus.
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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