Liouville theorem for one kind of elliptic equations on complete Riemannian manifold
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916506521042944 |
|---|---|
| author | Wu, Wangzhe |
| author_facet | Wu, Wangzhe |
| contents | We use maximum principle to prove the Liouville theorem of the equation $ΔU + b\cdot \nabla U + h U^α = 0, U \geq 0, 0 < α< \frac{n + 2}{n - 2}$ on the complete Riemannian manifold with non-negative Ricci tensor, which improve the result of Gidas-Spruck and Catino-Monticelli. We remark that this is the second version and all of the results come from the first version. Two months after we posted version 1 of this preprint on arXiv, we found Zhihao Lu has already posted a paper arXiv:2308.14764 before us and part of his result coincides with ours. So after deleting these parts and adding more reference and details, we post this second version on arXiv. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01063 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Liouville theorem for one kind of elliptic equations on complete Riemannian manifold Wu, Wangzhe Analysis of PDEs We use maximum principle to prove the Liouville theorem of the equation $ΔU + b\cdot \nabla U + h U^α = 0, U \geq 0, 0 < α< \frac{n + 2}{n - 2}$ on the complete Riemannian manifold with non-negative Ricci tensor, which improve the result of Gidas-Spruck and Catino-Monticelli. We remark that this is the second version and all of the results come from the first version. Two months after we posted version 1 of this preprint on arXiv, we found Zhihao Lu has already posted a paper arXiv:2308.14764 before us and part of his result coincides with ours. So after deleting these parts and adding more reference and details, we post this second version on arXiv. |
| title | Liouville theorem for one kind of elliptic equations on complete Riemannian manifold |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2311.01063 |