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<p>In this paper, we derive the a priori estimates for a class of more general (<i>k, l</i>)-Hessian quotient type equations involving <i>u</i> and <i>Du</i> 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 <i>k</i>-admissible solution for these general equations with the Neumann boundary condition, based on some growth conditions for the right hand function.</p>

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The a priori estimates for a class of general Hessian quotient type equations

  • 期刊论文

  • 发表日期：

    2025年3月11日

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  • Ni Xiang,
  • Yuni Xiong,
  • Jingyi Yao

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.