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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2505.10287 |
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| _version_ | 1866912377511870464 |
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| author | Lu, Siyuan Tsai, Yi-Lin |
| author_facet | Lu, Siyuan Tsai, Yi-Lin |
| contents | In this paper, we derive a Pogorelov type interior $C^2$ estimate for the Hessian quotient equation $\frac{σ_n}{σ_k}\left( D^2u\right) =f$. As an application, we show that convex viscosity solutions are regular for $k\leq n-3$ if $u\in C^{1,α}$ with $α>1-\frac{2}{n-k}$ or $u\in W^{2,p}$ with $p\geq\frac{(n-1)(n-k)}{2}$. Both exponents are sharp in view of the example in arXiv:2401.12229. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pogorelov type interior $C^2$ estimate for Hessian quotient equation and its application Lu, Siyuan Tsai, Yi-Lin Analysis of PDEs 35J60 In this paper, we derive a Pogorelov type interior $C^2$ estimate for the Hessian quotient equation $\frac{σ_n}{σ_k}\left( D^2u\right) =f$. As an application, we show that convex viscosity solutions are regular for $k\leq n-3$ if $u\in C^{1,α}$ with $α>1-\frac{2}{n-k}$ or $u\in W^{2,p}$ with $p\geq\frac{(n-1)(n-k)}{2}$. Both exponents are sharp in view of the example in arXiv:2401.12229. |
| title | Pogorelov type interior $C^2$ estimate for Hessian quotient equation and its application |
| topic | Analysis of PDEs 35J60 |
| url | https://arxiv.org/abs/2505.10287 |