The oblique boundary value problem for degenerate Hessian quotient type equations

Ni Xiang; Yuni Xiong; Lina Zheng

The oblique boundary value problem for degenerate Hessian quotient type equations

Analysis of PDEs 2025-07-21 v2

Authors: Ni Xiang , Yuni Xiong , Lina Zheng

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

Keywords

oblique boundary value problem degenerate Hessian quotient a priori estimates C^{1,1} solutions fully nonlinear PDE existence and uniqueness smooth bounded domain

Cite

@article{arxiv.2410.22856,
  title  = {The oblique boundary value problem for degenerate Hessian quotient type equations},
  author = {Ni Xiang and Yuni Xiong and Lina Zheng},
  journal= {arXiv preprint arXiv:2410.22856},
  year   = {2025}
}

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