Dirichlet problem for degenerate Hessian quotient type curvature equations

In the paper, we prove the existence and uniqueness results of the $C^{1,1}$ regular graphic hypersurface for Dirichlet problem of a class of degenerate Hessian quotient type curvature equations under the condition ${\psi }^{\frac{1}{k-l}}\in C^{1,1}(\bar{\mathrm{\Omega }}\times \mathbb{R}\times {\mathbb{S}}^n)$. Specially, we also consider the second order derivative estimates for the corresponding degenerate Hessian type curvature equations under the optimal condition ${\psi }^{\frac{1}{k-1}}\in C^{1,1}(\bar{\mathrm{\Omega }}\times \mathbb{R}\times {\mathbb{S}}^n)$.