Oblique boundary value problems for augmented Hessian equations II

被引：34

作者：

Jiang, Feida ^{[1
]}

Trudinger, Neil S. ^{[2
]}

机构：

[1] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

[2] Australian Natl Univ, Ctr Math & Its Applicat, Canberra, ACT 0200, Australia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 154卷

基金：

澳大利亚研究理事会; 中国博士后科学基金; 中国国家自然科学基金;

关键词：

Oblique boundary value problem; Augmented Hessian equations; a priori;

D O I：

10.1016/j.na.2016.08.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we continue our investigations into the global theory of oblique boundary value problems for augmented Hessian equations. We construct a global barrier function in terms of an admissible function in a uniform way when the matrix function in the augmented Hessian is only assumed regular. This enables us to derive global second derivative estimates in terms of boundary estimates which are then obtained by strengthening the concavity or monotonicity conditions in our previous work on the strictly regular case. Finally we give some applications to existence theorems which embrace standard Hessian equations as special cases. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：148 / 173

页数：26

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