{"title":"Notes on generalized special Lagrangian equation","authors":"XingChen Zhou","doi":"10.1007/s00526-024-02801-w","DOIUrl":null,"url":null,"abstract":"<p>We obtain a priori <span>\\(C^{1,1}\\)</span> estimates for some Hessian quotient equations with positive Lipschitz right hand sides, through studying a twisted special Lagrangian equation. The results imply the interior <span>\\(C^{2,\\alpha }\\)</span> regularity for <span>\\(C^0\\)</span> viscosity solutions to <span>\\(\\sigma _2=f^2(x)\\)</span> in dimension 3, with positive Lipschitz <i>f</i>(<i>x</i>).\n</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00526-024-02801-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
We obtain a priori \(C^{1,1}\) estimates for some Hessian quotient equations with positive Lipschitz right hand sides, through studying a twisted special Lagrangian equation. The results imply the interior \(C^{2,\alpha }\) regularity for \(C^0\) viscosity solutions to \(\sigma _2=f^2(x)\) in dimension 3, with positive Lipschitz f(x).
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