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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.17437 |
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| _version_ | 1866909764541218816 |
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| author | Huang, Yi Sui, Zhenan Xie, Mingyu |
| author_facet | Huang, Yi Sui, Zhenan Xie, Mingyu |
| contents | We solve the modified Gursky-Streets equation, which is a fully nonlinear equation arising in conformal geometry with uniform $C^{1, 1}$ estimates when (i) $γ> 0$ and $1 \leq k \leq n$ or (ii) $r > 0$ and $2 s k \leq r n$. We also prove the existence of a Lipschitz continuous viscosity solution when $r \neq 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of solution to modified Gursky-Streets equation Huang, Yi Sui, Zhenan Xie, Mingyu Analysis of PDEs We solve the modified Gursky-Streets equation, which is a fully nonlinear equation arising in conformal geometry with uniform $C^{1, 1}$ estimates when (i) $γ> 0$ and $1 \leq k \leq n$ or (ii) $r > 0$ and $2 s k \leq r n$. We also prove the existence of a Lipschitz continuous viscosity solution when $r \neq 0$. |
| title | Existence of solution to modified Gursky-Streets equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.17437 |