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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2501.05695 |
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| _version_ | 1866917889015021568 |
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| author | Gong, Jiabao Liu, Zixuan Tu, Qiang |
| author_facet | Gong, Jiabao Liu, Zixuan Tu, Qiang |
| contents | In this paper, we consider the Neumann problem for a class of Hessian quotient equations involving a gradient term on the right-hand side in Euclidean space. More precisely, we derive the interior gradient estimates for the $(Λ, k)$-convex solution of Hessian quotient equation $\frac{σ_k(Λ(D^2 u))}{σ_l(Λ(D^2 u))}=ψ(x,u,D u)$ with $0\leq l<k\leq C^{p-1}_{n-1}$ under the assumption of the growth condition. As an application, we obtain the global a priori estimates and the existence theorem for the Neumann problem of this Hessian quotient type equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Neumann problem for a class of Hessian quotient type equations Gong, Jiabao Liu, Zixuan Tu, Qiang Analysis of PDEs In this paper, we consider the Neumann problem for a class of Hessian quotient equations involving a gradient term on the right-hand side in Euclidean space. More precisely, we derive the interior gradient estimates for the $(Λ, k)$-convex solution of Hessian quotient equation $\frac{σ_k(Λ(D^2 u))}{σ_l(Λ(D^2 u))}=ψ(x,u,D u)$ with $0\leq l<k\leq C^{p-1}_{n-1}$ under the assumption of the growth condition. As an application, we obtain the global a priori estimates and the existence theorem for the Neumann problem of this Hessian quotient type equation. |
| title | The Neumann problem for a class of Hessian quotient type equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.05695 |