加权巴拿赫空间中的高阶椭圆方程

Q2 Mathematics

Annali dell''Universita di Ferrara Pub Date : 2024-03-15 DOI:10.1007/s11565-024-00505-9

Bilal T. Bilalov, Sabina R. Sadigova, Lyoubomira G. Softova

{"title":"加权巴拿赫空间中的高阶椭圆方程","authors":"Bilal T. Bilalov, Sabina R. Sadigova, Lyoubomira G. Softova","doi":"10.1007/s11565-024-00505-9","DOIUrl":null,"url":null,"abstract":"<div>We consider m-th order linear, uniformly elliptic equations \\(\\mathcal {L}u=f\\) with non-smooth coefficients in Banach–Sobolev spaces \\(W_{X_w}^m (\\Omega )\\) generated by weighted Banach Function Spaces (BFS) \\(X_w (\\Omega )\\) on a bounded domain \\(\\Omega \\subset {\\mathbb R}^{n}\\). Supposing boundedness of the Hardy–Littlewood Maximal operator and the Calderón–Zygmund singular integrals in \\(X_w (\\Omega )\\) we obtain solvability in the small in \\(W_{X_w}^m (\\Omega )\\) and establish interior Schauder type a priori estimates. These results will be used in order to obtain Fredholmness of the operator \\(\\mathcal {L}\\) in \\(X_w (\\Omega )\\).</div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1351 - 1373"},"PeriodicalIF":0.0000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00505-9.pdf","citationCount":"0","resultStr":"{\"title\":\"Higher order elliptic equations in weighted Banach spaces\",\"authors\":\"Bilal T. Bilalov, Sabina R. Sadigova, Lyoubomira G. Softova\",\"doi\":\"10.1007/s11565-024-00505-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We consider m-th order linear, uniformly elliptic equations \\\\(\\\\mathcal {L}u=f\\\\) with non-smooth coefficients in Banach–Sobolev spaces \\\\(W_{X_w}^m (\\\\Omega )\\\\) generated by weighted Banach Function Spaces (BFS) \\\\(X_w (\\\\Omega )\\\\) on a bounded domain \\\\(\\\\Omega \\\\subset {\\\\mathbb R}^{n}\\\\). Supposing boundedness of the Hardy–Littlewood Maximal operator and the Calderón–Zygmund singular integrals in \\\\(X_w (\\\\Omega )\\\\) we obtain solvability in the small in \\\\(W_{X_w}^m (\\\\Omega )\\\\) and establish interior Schauder type a priori estimates. These results will be used in order to obtain Fredholmness of the operator \\\\(\\\\mathcal {L}\\\\) in \\\\(X_w (\\\\Omega )\\\\).</div>\",\"PeriodicalId\":35009,\"journal\":{\"name\":\"Annali dell''Universita di Ferrara\",\"volume\":\"70 4\",\"pages\":\"1351 - 1373\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11565-024-00505-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali dell''Universita di Ferrara\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11565-024-00505-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali dell''Universita di Ferrara","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s11565-024-00505-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑在有界域\(\Omega \子集{\mathbb R}^{n}\)上由加权巴拿赫函数空间（BFS）\(X_w (\Omega )\) 生成的巴拿赫-索波列夫空间\(W_{X_w}^m (\Omega )\)中具有非光滑系数的 m 阶线性均匀椭圆方程（\mathcal {L}u=f\ ）。假设哈代-利特尔伍德（Hardy-Littlewood）最大算子和卡尔德龙-齐格蒙德（Calderón-Zygmund）奇异积分在\(X_w (\Omega )\) 中是有界的，我们就可以在\(W_{X_w}^m (\Omega )\) 中的小范围内获得可解性，并建立内部肖德尔（Schauder）型先验估计。这些结果将被用于获得在（X_w (\Omega )\) 中算子（\mathcal {L}\）的弗雷德霍尔姆性（Fredholmness）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Higher order elliptic equations in weighted Banach spaces

We consider m-th order linear, uniformly elliptic equations \(\mathcal {L}u=f\) with non-smooth coefficients in Banach–Sobolev spaces \(W_{X_w}^m (\Omega )\) generated by weighted Banach Function Spaces (BFS) \(X_w (\Omega )\) on a bounded domain \(\Omega \subset {\mathbb R}^{n}\). Supposing boundedness of the Hardy–Littlewood Maximal operator and the Calderón–Zygmund singular integrals in \(X_w (\Omega )\) we obtain solvability in the small in \(W_{X_w}^m (\Omega )\) and establish interior Schauder type a priori estimates. These results will be used in order to obtain Fredholmness of the operator \(\mathcal {L}\) in \(X_w (\Omega )\).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annali dell''Universita di Ferrara Mathematics-Mathematics (all)

CiteScore

1.70

自引率

0.00%

发文量

期刊介绍： Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.