{"title":"关于广义特殊拉格朗日方程的说明","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":"{\"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}","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}
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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