Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

Chenyang Liu; Jing Mao; Yating Zhao

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arXiv · 2201.08644

Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

Chenyang Liu·Jing Mao·Yating Zhao

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Abstract

Let $\Omega$ be a bounded domain (with smooth boundary) on the hyperbolic plane $\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$. In this paper, by using a priori estimates, we can establish Pogorelov type estimates of $k$-convex solutions to a class of Hessian quotient equations defined over $\Omega\subset\mathscr{H}^{n}(1)$ and with the vanishing Dirichlet boundary condition.

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Chenyang Liu, Jing Mao, Yating Zhao. 2022-01-21. Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$. https://arxiv.org/abs/2201.08644

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