{"title":"Global Weighted Lorentz Estimates of Oblique Tangential Derivative Problems for Weakly Convex Fully Nonlinear Operators","authors":"Junior da S. Bessa, Gleydson C. Ricarte","doi":"10.1007/s11118-024-10156-2","DOIUrl":null,"url":null,"abstract":"<p>In this work, we develop weighted Lorentz-Sobolev estimates for viscosity solutions of fully nonlinear elliptic equations with oblique boundary condition under weakened convexity conditions in the following configuration: </p><span>$$\\left\\{ \\begin{array}{rclcl} F(D^2u,Du,u,x) & =& f(x)& \\text {in} & \\Omega \\\\ \\beta \\cdot Du + \\gamma u& =& g & \\text {on}& \\partial \\Omega ,\\end{array}\\right. $$</span><p>where <span>\\(\\Omega \\)</span> is a bounded domain in <span>\\(\\mathbb {R}^{n}\\)</span> (<span>\\(n\\ge 2\\)</span>), under suitable assumptions on the source term <i>f</i>, data <span>\\(\\beta , \\gamma \\)</span> and <i>g</i>. In addition, we obtain Lorentz-Sobolev estimates for solutions to the obstacle problem and others applications.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11118-024-10156-2","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we develop weighted Lorentz-Sobolev estimates for viscosity solutions of fully nonlinear elliptic equations with oblique boundary condition under weakened convexity conditions in the following configuration:
where \(\Omega \) is a bounded domain in \(\mathbb {R}^{n}\) (\(n\ge 2\)), under suitable assumptions on the source term f, data \(\beta , \gamma \) and g. In addition, we obtain Lorentz-Sobolev estimates for solutions to the obstacle problem and others applications.
期刊介绍:
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