{"title":"The anisotropic convexity of domains and the boundary estimate for two Monge–Ampère equations","authors":"Ruosi Chen , Huaiyu Jian","doi":"10.1016/j.na.2024.113580","DOIUrl":null,"url":null,"abstract":"<div><p>We study the exact effect of the anisotropic convexity of domains on the boundary estimate for two Monge–Ampère Equations: one is singular which is from the proper affine hyperspheres with constant mean curvature; the other is degenerate which is from the Monge–Ampère eigenvalue problem. As a result, we obtain the sharp boundary estimates and the optimal global Hölder regularity for the two equations.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"245 ","pages":"Article 113580"},"PeriodicalIF":1.3000,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24000993","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the exact effect of the anisotropic convexity of domains on the boundary estimate for two Monge–Ampère Equations: one is singular which is from the proper affine hyperspheres with constant mean curvature; the other is degenerate which is from the Monge–Ampère eigenvalue problem. As a result, we obtain the sharp boundary estimates and the optimal global Hölder regularity for the two equations.
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