The oblique boundary value problem for degenerate Hessian quotient type equations

In this paper, we investigate the oblique boundary value problem for degenerate Hessian quotient type equations in a smooth bounded domain. Without imposing any geometric restrictions on the domain, we establish the a priori estimates and derive the existence and uniqueness of admissible $C^{1,1}$ solutions under the condition $f^{\frac{1}{k-l}}\in C^{1,1}(\bar{\mathrm{\Omega }}\times \mathbb{R})$.