Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917055281758208 |
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| author | Dong, Weisong Li, Yanyan Nguyen, Luc |
| author_facet | Dong, Weisong Li, Yanyan Nguyen, Luc |
| contents | In this paper, we consider the Dirichlet boundary value problem for fully nonlinear Yamabe equations on Riemannian manifolds with boundary. Assuming the existence of a subsolution, we derive \emph{a priori} boundary second derivative estimates and consequently obtain the existence of a smooth solution. Moreover, with respect to a family of equations interpolating the fully nonlinear Yamabe equation and the classical semi-linear Yamabe equation, our estimates remain uniform. Finally, an example of a $C^1$ solution which is smooth in the interior but not smooth at the boundary is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds Dong, Weisong Li, Yanyan Nguyen, Luc Analysis of PDEs Differential Geometry 35J60, 35B45, 53C18, 53C21 In this paper, we consider the Dirichlet boundary value problem for fully nonlinear Yamabe equations on Riemannian manifolds with boundary. Assuming the existence of a subsolution, we derive \emph{a priori} boundary second derivative estimates and consequently obtain the existence of a smooth solution. Moreover, with respect to a family of equations interpolating the fully nonlinear Yamabe equation and the classical semi-linear Yamabe equation, our estimates remain uniform. Finally, an example of a $C^1$ solution which is smooth in the interior but not smooth at the boundary is also given. |
| title | Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds |
| topic | Analysis of PDEs Differential Geometry 35J60, 35B45, 53C18, 53C21 |
| url | https://arxiv.org/abs/2511.01130 |