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 \(\psi ^{\frac{1}{k-l}}\in C^{1,1}(\overline{\Omega }\times \mathbb {R}\times \mathbb {S}^n)\) . Specially, we also consider the second order derivative estimates for the corresponding degenerate Hessian type curvature equations under the optimal condition \(\psi ^{\frac{1}{k-1}}\in C^{1,1}(\overline{\Omega }\times \mathbb {R}\times \mathbb {S}^n)\) .
