The exterior Dirichlet problem for special Lagrangian equations in dimensions n ≤ 4

被引：5

作者：

Bao, Jiguang ^{[1
]}

Li, Haigang ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2013年 / 89卷

关键词：

Special Lagrangian equation; Hessian quotient equation; Exterior Dirichlet problem; Viscosity solution; VISCOSITY SOLUTIONS; MAXIMUM PRINCIPLE; BERNSTEIN PROBLEM; EXISTENCE; REGULARITY; UNIQUENESS; EXTENSION; THEOREM;

D O I：

10.1016/j.na.2013.05.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish the existence theorem for the exterior Dirichlet problem for special Lagrangian equations with prescribed asymptotic behavior at infinity. This extends the previous results on Monge-Ampere equations and Hessian equations to special Lagrangian equations in dimensions n <= 4, which is from calibrated geometry. More generally, we prove that the result is also true for Hessian quotient equations with 0 <= l < k <= n in dimensions n >= 3. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：219 / 229

页数：11

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