  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
$\psi^{\frac{1}{k-1}}\in
C^{1,1}(\overline{\Omega}\times\mathbb{R}\times\mathbb{S}^n)$.
