The oblique boundary value problem for degenerate Hessian quotient type equations

TL;DR

This paper studies the oblique boundary value problem for degenerate Hessian quotient equations, establishing a priori estimates and proving existence and uniqueness of solutions without geometric restrictions.

Contribution

It introduces new methods to obtain a priori estimates and proves existence and uniqueness of solutions for degenerate Hessian quotient equations without domain restrictions.

Findings

Established a priori estimates for solutions.

Proved existence and uniqueness of admissible solutions.

Solutions are in $C^{1,1}$ under specified conditions.

Abstract

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