{"title":"The Liouville theorem for Sum Hessian equations in half spaces","authors":"Xiaobiao Jia , Shanshan Ma","doi":"10.1016/j.na.2024.113692","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we consider the Liouville theorem for <span><math><mi>k</mi></math></span>-convex solutions to Sum Hessian equations in half spaces. The key is to show the Pogorelov type estimate up to the flat boundary.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113692"},"PeriodicalIF":1.3000,"publicationDate":"2024-11-02","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/S0362546X24002116","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
In this paper, we consider the Liouville theorem for -convex solutions to Sum Hessian equations in half spaces. The key is to show the Pogorelov type estimate up to the flat boundary.
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