THE A PRIORI ESTIMATES FOR A CLASS OF GENERAL HESSIAN QUOTIENT TYPE EQUATIONS

doi:10.1007/s10473-025-0308-2

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (3): 867-884.doi: 10.1007/s10473-025-0308-2

THE A PRIORI ESTIMATES FOR A CLASS OF GENERAL HESSIAN QUOTIENT TYPE EQUATIONS

Ni XIANG, Yuni XIONG^†, Jingyi YAO

Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China

收稿日期:2023-09-27 修回日期:2024-05-01 出版日期:2025-05-25 发布日期:2025-09-30

THE A PRIORI ESTIMATES FOR A CLASS OF GENERAL HESSIAN QUOTIENT TYPE EQUATIONS

Ni XIANG, Yuni XIONG^†, Jingyi YAO

Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China

Received:2023-09-27 Revised:2024-05-01 Online:2025-05-25 Published:2025-09-30
Contact: ^†Yuni XIONG, E-mail: 202121104011767@stu.hubu.edu.cn;
About author:Ni XIANG, E-mail: nixiang@hubu.edu.cn; Jingyi YAO, E-mail: 202121104011748@stu.hubu.edu.cn
Supported by:
National Natural Science Foundation of China (No. 11971157).

摘要/Abstract

摘要： In this paper, we derive the a priori estimates for a class of more general $(k,l)$-Hessian quotient type equations involving $u$ and $Du$ on the right hand function. As an application we prove the Liouville theorem depending on Pogorelov type estimates. On the other hand, we obtain the existence and uniqueness of the $k$-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.

关键词: Hessian quotient type equations, the a priori estimates, Neumann problems, Liouville Theorem

Abstract: In this paper, we derive the a priori estimates for a class of more general $(k,l)$-Hessian quotient type equations involving $u$ and $Du$ on the right hand function. As an application we prove the Liouville theorem depending on Pogorelov type estimates. On the other hand, we obtain the existence and uniqueness of the $k$-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.

Key words: Hessian quotient type equations, the a priori estimates, Neumann problems, Liouville Theorem

中图分类号:

35J60

Ni XIANG, Yuni XIONG, Jingyi YAO. THE A PRIORI ESTIMATES FOR A CLASS OF GENERAL HESSIAN QUOTIENT TYPE EQUATIONS[J]. 数学物理学报(英文版), 2025, 45(3): 867-884.

Ni XIANG, Yuni XIONG, Jingyi YAO. THE A PRIORI ESTIMATES FOR A CLASS OF GENERAL HESSIAN QUOTIENT TYPE EQUATIONS[J]. Acta mathematica scientia,Series B, 2025, 45(3): 867-884.

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THE A PRIORI ESTIMATES FOR A CLASS OF GENERAL HESSIAN QUOTIENT TYPE EQUATIONS

THE A PRIORI ESTIMATES FOR A CLASS OF GENERAL HESSIAN QUOTIENT TYPE EQUATIONS

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