Interior Hessian estimates for a class of Hessian type equations

被引：13

作者：

Chen, Chuanqiang ^{[1
]}

Dong, Weisong ^{[2
]}

Han, Fei ^{[3
]}

机构：

[1] Ningbo Univ, Sch Math & Stat, Ningbo 315211, Zhejiang, Peoples R China

[2] Tianjin Univ, Sch Math, Tianjin 300354, Peoples R China

[3] Xinjiang Normal Univ, Sch Math Sci, Urumqi 830054, Xinjiang Uygur, Peoples R China

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 62卷 / 02期

关键词：

Primary; 35B45; Secondary; 35J60; ELLIPTIC-EQUATIONS; DIRICHLET PROBLEM; NEUMANN PROBLEM; PLURISUBHARMONICITY; CONVEXITY; EXISTENCE;

D O I：

10.1007/s00526-022-02385-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce some Hessian operators sigma k(eta) and sigma k(eta)/sigma l(eta) by a self-adjoint mapping and the corresponding convex cone (sic)k, and derive interior a priori Hessian estimates for the equ ation sigma k(eta) sigma l(eta) = f (x) in (sic)k with 0 <= l < k < n. As an application we prove Pogorelov type estimates which imply Liouville theorem for such equation.

引用

页数：15

共 50 条

[31] An interior second derivative bound for solutions of Hessian equations
John Urbas
Calculus of Variations and Partial Differential Equations, 2001, 12 : 417 - 431
[32] Some interior regularity results for solutions of Hessian equations
Urbas, J
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2000, 11 (01) : 1 - 31
[33] Some interior regularity results for solutions of Hessian equations
John Urbas
Calculus of Variations and Partial Differential Equations, 2000, 11 : 1 - 31
[34] An interior second derivative bound for solutions of Hessian equations
Urbas, J
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2001, 12 (04) : 417 - 431
[35] The Lp Minkowski type problem for a class of mixed Hessian quotient equations
Chen, Chuanqiang
Xu, Lu
ADVANCES IN MATHEMATICS, 2022, 411
[36] Weak Solutions to Complex Hessian Type Equations in the Class εφ(X, ω, m)
Amal, Hichame
Asserda, Said
El-Gasmi, Ayoub
VIETNAM JOURNAL OF MATHEMATICS, 2024, 52 (01) : 117 - 128
[37] Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations
Gao, Zhenghuan
Jia, Xiaohan
Zhang, Dekai
JOURNAL OF GEOMETRIC ANALYSIS, 2023, 33 (05)
[38] Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations
Zhenghuan Gao
Xiaohan Jia
Dekai Zhang
The Journal of Geometric Analysis, 2023, 33
[39] A class of Hessian quotient equations in Euclidean space
Chen, Xiaojuan
Tu, Qiang
Xiang, Ni
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (12) : 11172 - 11194
[40] Regularity for a Class of Singular Complex Hessian Equations
Jia Xiang Wang
Bin Zhou
Acta Mathematica Sinica, English Series, 2021, 37 : 1709 - 1720

← 1 2 3 4 5 →