ON THE EXTERIOR DIRICHLET PROBLEM FOR HESSIAN EQUATIONS

被引：31

作者：

Bao, Jiguang ^{[1
]}

Li, Haigang ^{[1
]}

Li, Yanyan ^{[2
]}

机构：

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

[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 366卷 / 12期

关键词：

VISCOSITY SOLUTIONS; MAXIMUM PRINCIPLE; EXISTENCE; UNIQUENESS; EXTENSION; THEOREM;

D O I：

10.1090/S0002-9947-2014-05867-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish a theorem on the existence of the solutions of the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity. This extends a result of Caffarelli and Li (2003) for the Monge-Ampere equation to Hessian equations.

引用

页码：6183 / 6200

页数：18

共 50 条

[1] The exterior Dirichlet problem for Hessian quotient equations
Li, Haigang
Dai, Limei
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 393 (02) : 534 - 543
[2] On the exterior Dirichlet problem for Hessian quotient equations
Li, Dongsheng
Li, Zhisu
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (11) : 6633 - 6662
[3] The Dirichlet problem for Hessian quotient equations in exterior domains
Dai, Limei
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 380 (01) : 87 - 93
[4] The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations
Dai, Limei
[J]. ANALYSIS IN THEORY AND APPLICATIONS, 2022,
[5] The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations
Dai, Limei
[J]. ANALYSIS IN THEORY AND APPLICATIONS, 2023, 39 (02) : 120 - 146
[6] The Dirichlet Problem of Hessian Equation in Exterior Domains
Li, Hongfei
Dai, Limei
[J]. MATHEMATICS, 2020, 8 (05)
[7] Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations
Limei Dai
Hongfei Li
[J]. Boundary Value Problems, 2022
[8] The exterior Dirichlet problem for fully nonlinear elliptic equations related to the eigenvalues of the Hessian
Li, Haigang
Bao, Jiguang
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (07) : 2480 - 2501
[9] On the Dirichlet problem for Hessian equations
Trudinger, NS
[J]. ACTA MATHEMATICA, 1995, 175 (02) : 151 - 164
[10] On the exterior Dirichlet problem for Hessian-type fully nonlinear elliptic equations
Li, Xiaoliang
Wang, Cong
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2024, 26 (04)

← 1 2 3 4 5 →