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

共 50 条

[21] The Neumann Problem for Special Lagrangian Equations with Critical Phase
Wang, Jun
COMMUNICATIONS IN MATHEMATICS AND STATISTICS, 2019, 7 (03) : 329 - 361
[22] The Neumann problem of special Lagrangian equations with supercritical phase
Chen, Chuanqiang
Ma, Xinan
Wei, Wei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (09) : 5388 - 5409
[23] The Neumann Problem for Special Lagrangian Equations with Critical Phase
Jun Wang
Communications in Mathematics and Statistics, 2019, 7 : 329 - 361
[24] On the exterior Dirichlet problem for Hessian-type fully nonlinear elliptic equations
Li, Xiaoliang
Wang, Cong
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2024, 26 (04)
[25] ASYMPTOTICS OF THE SOLUTION OF THE DIRICHLET PROBLEM FOR THE LAPLACE AND HELMHOLTZ EQUATIONS IN THE EXTERIOR OF A SLENDER CYLINDER
FEDORJUK, MV
MATHEMATICS OF THE USSR-IZVESTIYA, 1981, 45 (01): : 145 - 161
[26] Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations
Dai, Limei
Li, Hongfei
BOUNDARY VALUE PROBLEMS, 2022, 2022 (01)
[27] Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations
Limei Dai
Hongfei Li
Boundary Value Problems, 2022
[28] The exterior Dirichlet problem for fully nonlinear elliptic equations related to the eigenvalues of the Hessian
Li, Haigang
Bao, Jiguang
JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (07) : 2480 - 2501
[29] EXTERIOR DIRICHLET PROBLEM FOR HELMHOLTZ EQUATION
AHNER, JF
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1975, 52 (03) : 415 - 429
[30] SINGULAR PERTURBATION OF AN EXTERIOR DIRICHLET PROBLEM
HSIAO, GC
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1978, 9 (01) : 160 - 184

← 1 2 3 4 5 →