Dirichlet problem for degenerate Hessian quotient type curvature equations

In the paper, we prove the existence and uniqueness results of the C1,1 regular graphic hypersurface for Dirichlet problem of a class of degenerate Hessian quotient type curvature equations under the condition ψ1/k-l∈ C1,1(Ω̄ⁿ). Specially, we also consider the second order derivative estimates for the corresponding degenerate Hessian type curvature equations under the optimal condition ψ1/k-1∈ C1,1(Ω̄ⁿ).