{"title":"Boundary estimates of solutions mixed boundary problems for elliptic\nequations with VMO coefficients","authors":"Konul G. Suleymanova","doi":"10.30546/2706-7734.43.7.2023.84","DOIUrl":null,"url":null,"abstract":". In this paper we obtain generalized weighted Sobolev – Morrey estimates with weights from the Muckenhoupt class A p by establishing boundedness of several important operators in harmonic analysis such as Hardy – Littlewood operators and Calderon –Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions mixed boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev – Morrey spaces in a smooth bounded domain Ω ⊂ R n are obtained.","PeriodicalId":38552,"journal":{"name":"Engineering Transactions","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Transactions","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30546/2706-7734.43.7.2023.84","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
. In this paper we obtain generalized weighted Sobolev – Morrey estimates with weights from the Muckenhoupt class A p by establishing boundedness of several important operators in harmonic analysis such as Hardy – Littlewood operators and Calderon –Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions mixed boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev – Morrey spaces in a smooth bounded domain Ω ⊂ R n are obtained.
期刊介绍：
Engineering Transactions (formerly Rozprawy Inżynierskie) is a refereed international journal founded in 1952. The journal promotes research and practice in engineering science and provides a forum for interdisciplinary publications combining mechanics with: Material science, Mechatronics, Biomechanics and Biotechnologies, Environmental science, Photonics, Information technologies, Other engineering applications. The journal publishes original papers covering a broad area of research activities including: experimental and hybrid techniques, analytical and numerical approaches. Review articles and special issues are also welcome. Following long tradition, all articles are peer reviewed and our expert referees ensure that the papers accepted for publication comply with high scientific standards. Engineering Transactions is a quarterly journal intended to be interesting and useful for the researchers and practitioners in academic and industrial communities.
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