Journal article
Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds
- Abstract:
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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 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 C1 solution which is smooth in the interior but not smooth at the boundary is also given.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 341.4KB, Terms of use)
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- Publisher copy:
- 10.3934/dcds.2026100
Authors
- Publisher:
- American Institute of Mathematical Sciences
- Journal:
- Discrete and Continuous Dynamical Systems More from this journal
- Publication date:
- 2026-05-18
- Acceptance date:
- 2026-05-05
- DOI:
- EISSN:
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1553-5231
- ISSN:
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1078-0947
- Language:
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English
- Keywords:
- Pubs id:
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2415068
- Local pid:
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pubs:2415068
- Deposit date:
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2026-05-05
- ARK identifier:
Terms of use
- Copyright holder:
- American Institute of Mathematical Sciences
- Copyright date:
- 2026
- Rights statement:
- Copyright © 2026 American Institute of Mathematical Sciences
- Notes:
- The author accepted manuscript (AAM) of this paper has been made available under the University of Oxford's Open Access Publications Policy, and a CC BY public copyright licence has been applied.
- Licence:
- CC Attribution (CC BY)
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