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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.09044 |
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| _version_ | 1866913021105799168 |
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| author | Gong, Jiabao Tu, Qiang |
| author_facet | Gong, Jiabao Tu, Qiang |
| contents | In this paper, we obtain some important inequalities for a class of Hessian quotient type operators $\frac{σ_k(Λ(D^2u))}{σ_l(Λ(D^2u))}$, which can be regarded as a generalization of the classical Hessian quotient operators. As an application, we establish global a priori estimates and prove an existence theorem for the Neumann problem of the corresponding degenerate Hessian quotient type equation, in which the admissible range of $k$ is extended to $0< k \leq C^\mathbf{p}_n$ with $1 \leq \mathbf{p} \leq n-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09044 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Neumann problem for a class of degenerate Hessian quotient type equations Gong, Jiabao Tu, Qiang Analysis of PDEs In this paper, we obtain some important inequalities for a class of Hessian quotient type operators $\frac{σ_k(Λ(D^2u))}{σ_l(Λ(D^2u))}$, which can be regarded as a generalization of the classical Hessian quotient operators. As an application, we establish global a priori estimates and prove an existence theorem for the Neumann problem of the corresponding degenerate Hessian quotient type equation, in which the admissible range of $k$ is extended to $0< k \leq C^\mathbf{p}_n$ with $1 \leq \mathbf{p} \leq n-1$. |
| title | The Neumann problem for a class of degenerate Hessian quotient type equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.09044 |