The Dirichlet problem for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

Abstract

In this paper, under suitable settings, we can obtain the existence and uniqueness of solutions to a class of Hessian quotient equations with Dirichlet boundary condition in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, which can be seen as a prescribed curvature problem and a continuous work of [12].