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arXiv · 2410.22856

The oblique boundary value problem for degenerate Hessian quotient type equations

Ni Xiang·Yuni Xiong·Lina Zheng
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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 $f^{\frac{1}{k-l}}\in C^{1,1}(\overline{\Omega}\times\mathbb{R})$.

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Ni Xiang, Yuni Xiong, Lina Zheng. 2024-10-30. The oblique boundary value problem for degenerate Hessian quotient type equations. https://doi.org/10.1142/s0219199726500707

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