GLOBAL REGULARITY FOR A CLASS OF MONGE-AMPERE TYPE EQUATIONS WITH NONZERO BOUNDARY CONDITIONS

被引：0
作者：
Li, Mengni [1 ,2 ]
机构：
[1] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China
[2] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 01期
关键词：
Monge-Ampere type equation; Dirichlet problem; convex domain; Hiilder estimate; boundary regularity; DIRICHLET PROBLEM; SMOOTHNESS;
D O I：
10.3934/cpaa.2020267
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the boundary regularity of solutions to the Dirichlet problem for a class of Monge-Ampere type equations with nonzero boundary conditions. We construct global Holder estimates for convex solutions to the problem and emphasize that the boundary regularity essentially depends on the convexity of the domain. The proof is based on a careful study of the concept of (a, eta) type convex domain and a family of auxiliary functions.
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页码：301 / 317
页数：17
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