Optimal Liouville theorems for the Lane-Emden equation on Riemannian manifolds
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912741599477760 |
|---|---|
| author | He, Jie Sun, Linlin Wang, Youde |
| author_facet | He, Jie Sun, Linlin Wang, Youde |
| contents | We study degenerate quasilinear elliptic equations on Riemannian manifolds and obtain several Liouville theorems. Notably, we provide rigorous proof asserting the nonexistence of positive solutions to the subcritical Lane-Emden-Fowler equations over complete Riemannian manifolds with nonnegative Ricci curvature. These findings serve as a significant generalization of Gidas and Spruck's pivotal work (Comm. Pure Appl. Math. 34, 525-598, 1981) which focused on the semilinear case, as well as Serrin and Zou's contributions (Acta Math. 189, 79-142, 2002) within the context of Euclidean geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Liouville theorems for the Lane-Emden equation on Riemannian manifolds He, Jie Sun, Linlin Wang, Youde Analysis of PDEs Primary 58J05, 35B53, 35J92, Secondary 35B45, 35B08, 35B09 We study degenerate quasilinear elliptic equations on Riemannian manifolds and obtain several Liouville theorems. Notably, we provide rigorous proof asserting the nonexistence of positive solutions to the subcritical Lane-Emden-Fowler equations over complete Riemannian manifolds with nonnegative Ricci curvature. These findings serve as a significant generalization of Gidas and Spruck's pivotal work (Comm. Pure Appl. Math. 34, 525-598, 1981) which focused on the semilinear case, as well as Serrin and Zou's contributions (Acta Math. 189, 79-142, 2002) within the context of Euclidean geometries. |
| title | Optimal Liouville theorems for the Lane-Emden equation on Riemannian manifolds |
| topic | Analysis of PDEs Primary 58J05, 35B53, 35J92, Secondary 35B45, 35B08, 35B09 |
| url | https://arxiv.org/abs/2411.06956 |