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arXiv · 2501.05695

The Neumann problem for a class of Hessian quotient type equations

Jiabao Gong·Zixuan Liu·Qiang Tu
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Abstract

In this paper, we consider the Neumann problem for a class of Hessian quotient equations involving a gradient term on the right-hand side in Euclidean space. More precisely, we derive the interior gradient estimates for the $(\Lambda, k)$-convex solution of Hessian quotient equation $\frac{\sigma_k(\Lambda(D^2 u))}{\sigma_l(\Lambda(D^2 u))}=\psi(x,u,D u)$ with $0\leq l<k\leq C^{p-1}_{n-1}$ under the assumption of the growth condition. As an application, we obtain the global a priori estimates and the existence theorem for the Neumann problem of this Hessian quotient type equation.

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Jiabao Gong, Zixuan Liu, Qiang Tu. 2025-01-10. The Neumann problem for a class of Hessian quotient type equations. https://arxiv.org/abs/2501.05695

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