Pogorelov type estimates for $(n-1)$-Hessian equations and related rigidity theorems
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912170984341504 |
|---|---|
| author | Tu, Qiang |
| author_facet | Tu, Qiang |
| contents | In this paper, we establish Pogorelov type $C^2$ estimates for admissible solutions to the Dirichlet problem of $(n-1)$-Hessian equation based on a concavity inequality, which is inspired by the Lu-Tsai's work on the global curvature estimates for the $n-1$ curvature equation. As an application, we apply such estimates to obtain a rigidity theorems for admissible solutions of $(n-1)$-Hessian equation only under quadratic growth conditions. This result gives a positive answer to a open problem for $k$-Hessian equation, which is proposed by Chang-Yuan, in case $k=n-1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pogorelov type estimates for $(n-1)$-Hessian equations and related rigidity theorems Tu, Qiang Analysis of PDEs 35J60, 35B45 In this paper, we establish Pogorelov type $C^2$ estimates for admissible solutions to the Dirichlet problem of $(n-1)$-Hessian equation based on a concavity inequality, which is inspired by the Lu-Tsai's work on the global curvature estimates for the $n-1$ curvature equation. As an application, we apply such estimates to obtain a rigidity theorems for admissible solutions of $(n-1)$-Hessian equation only under quadratic growth conditions. This result gives a positive answer to a open problem for $k$-Hessian equation, which is proposed by Chang-Yuan, in case $k=n-1$. |
| title | Pogorelov type estimates for $(n-1)$-Hessian equations and related rigidity theorems |
| topic | Analysis of PDEs 35J60, 35B45 |
| url | https://arxiv.org/abs/2405.02939 |