{"title":"Nonlinear weighted elliptic problem with variable exponents and $$L^1$$ data","authors":"Rabah Mecheter","doi":"10.1007/s13226-024-00627-y","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we prove the existence of weak solutions for a class of nonlinear weighted elliptic equations in <span>\\(\\Omega \\)</span> with <i>p</i>(<i>x</i>) growth conditions and integrable data. The functional setting involves Lebesgue-Sobolev spaces with variable exponents. Our results are generalizations of the corresponding results in the constant exponent case in L. Boccardo et al (Boll. Unione Mat. Ital. 15, No. 4, 503-514 (2022)) and some results given in D. Arcoya et al ( Journal of Functional Analysis, 268(5), 1153-1166 (2015)).</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00627-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we prove the existence of weak solutions for a class of nonlinear weighted elliptic equations in \(\Omega \) with p(x) growth conditions and integrable data. The functional setting involves Lebesgue-Sobolev spaces with variable exponents. Our results are generalizations of the corresponding results in the constant exponent case in L. Boccardo et al (Boll. Unione Mat. Ital. 15, No. 4, 503-514 (2022)) and some results given in D. Arcoya et al ( Journal of Functional Analysis, 268(5), 1153-1166 (2015)).
本文证明了一类具有 p(x) 增长条件和可积分数据的 \(\Omega \) 非线性加权椭圆方程的弱解存在性。函数设置涉及具有可变指数的 Lebesgue-Sobolev 空间。我们的结果是 L. Boccardo et al (Boll. Unione Mat.Unione Mat.Ital.15, No. 4, 503-514 (2022)) 和 D. Arcoya et al ( Journal of Functional Analysis, 268(5), 1153-1166 (2015)) 中给出的一些结果。
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