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

  • Ni XIANG ,
  • Yuni XIONG ,
  • Jingyi YAO
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  • Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China
Ni XIANG, E-mail: nixiang@hubu.edu.cn; Jingyi YAO, E-mail: 202121104011748@stu.hubu.edu.cn

Received date: 2023-09-27

  Revised date: 2024-05-01

  Online published: 2025-09-30

Supported by

National Natural Science Foundation of China (No. 11971157).

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.

Cite this article

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 . DOI: 10.1007/s10473-025-0308-2

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