Dirichlet problem for degenerate Hessian quotient type curvature equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913342748098560 |
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| author | Chen, Xiaojuan Tu, Qiang Xiang, Ni |
| author_facet | Chen, Xiaojuan Tu, Qiang Xiang, Ni |
| contents | In the paper, we prove the existence and uniqueness results of the $C^{1,1}$ regular graphic hypersurface for Dirichlet problem of a class of degenerate Hessian quotient type curvature equations under the condition $ψ^{\frac{1}{k-l}}\in C^{1,1}(\overlineΩ\times\mathbb{R}\times\mathbb{S}^n)$. Specially, we also consider the second order derivative estimates for the corresponding degenerate Hessian type curvature equations under the optimal condition $ψ^{\frac{1}{k-1}}\in C^{1,1}(\overlineΩ\times\mathbb{R}\times\mathbb{S}^n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dirichlet problem for degenerate Hessian quotient type curvature equations Chen, Xiaojuan Tu, Qiang Xiang, Ni Analysis of PDEs 35J70, 35J15 In the paper, we prove the existence and uniqueness results of the $C^{1,1}$ regular graphic hypersurface for Dirichlet problem of a class of degenerate Hessian quotient type curvature equations under the condition $ψ^{\frac{1}{k-l}}\in C^{1,1}(\overlineΩ\times\mathbb{R}\times\mathbb{S}^n)$. Specially, we also consider the second order derivative estimates for the corresponding degenerate Hessian type curvature equations under the optimal condition $ψ^{\frac{1}{k-1}}\in C^{1,1}(\overlineΩ\times\mathbb{R}\times\mathbb{S}^n)$. |
| title | Dirichlet problem for degenerate Hessian quotient type curvature equations |
| topic | Analysis of PDEs 35J70, 35J15 |
| url | https://arxiv.org/abs/2405.03422 |