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arXiv · 2604.09044

The Neumann problem for a class of degenerate Hessian quotient type equations

Jiabao Gong·Qiang Tu
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Abstract

In this paper, we obtain some important inequalities for a class of Hessian quotient type operators $\frac{\sigma_k(\Lambda(D^2u))}{\sigma_l(\Lambda(D^2u))}$, which can be regarded as a generalization of the classical Hessian quotient operators. As an application, we establish global a priori estimates and prove an existence theorem for the Neumann problem of the corresponding degenerate Hessian quotient type equation, in which the admissible range of $k$ is extended to $0< k \leq C^\mathbf{p}_n$ with $1 \leq \mathbf{p} \leq n-1$.

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Jiabao Gong, Qiang Tu. 2026-04-10. The Neumann problem for a class of degenerate Hessian quotient type equations. https://arxiv.org/abs/2604.09044

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