{"title":"Gradient estimate for solutions of second-order elliptic equations","authors":"V. Maz'ya, R. McOwen","doi":"10.57262/ade027-0102-77","DOIUrl":null,"url":null,"abstract":"We obtain a local estimate for the gradient of solutions to a second-order elliptic equation in divergence form with bounded measurable coefficients that are square-Dini continuous at the single point x = 0. In particular, we treat the case of solutions that are not Lipschitz continuous at x = 0. We show that our estimate is sharp.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.57262/ade027-0102-77","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We obtain a local estimate for the gradient of solutions to a second-order elliptic equation in divergence form with bounded measurable coefficients that are square-Dini continuous at the single point x = 0. In particular, we treat the case of solutions that are not Lipschitz continuous at x = 0. We show that our estimate is sharp.
期刊介绍：
Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.
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