Boundary Regularity for k-Hessian Equations

作     者：You LI Meng Ni LI Yan Nan LIU You LI;Meng Ni LI;Yan Nan LIU

作者机构：School of Mathematics and Computational SciencesXiangtan UniversityHunan 411105P.R.China School of MathematicsSoutheast UniversityNanjing 211189P.R.China School of Mathematics and StatisticsBeijing Technology and Business UniversityBeijing 100048P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2023年第39卷第12期

页      面：2393-2413页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported in part by Natural Science Foundation of Beijing Municipality(Grant No.1212002) National Natural Science Foundation of China(Grant Nos.12071017,12141103,12301263 and 12201107) Fundamental Research Funds for the Central Universities(Grant No.2242023R40041) 

主　　题：Dirichlet problem k-Hessian equation symmetric mean 

摘      要：In this paper we focus on the boundary regularity for a class of k-Hessian equations which can be degenerate and(or)singular on the boundary of the *** by the case of Monge-Ampere equations,we first construct sub-solutions,then apply the characteristic of the global Holder continuity for convex functions,and finally use the maximum principle to obtain the boundary Holder continuity for the solutions of the k-Hessian ***,finding such sub-solutions is very difficult due to the complexity of the k-Hessian *** particular,we employ the symmetric mean to overcome the difficulties.