Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in $\mathbb R^n$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917872036478976 |
|---|---|
| author | Ma, Xi-Nan Wu, Wangzhe |
| author_facet | Ma, Xi-Nan Wu, Wangzhe |
| contents | We improve the Liouville theorem for the equation $-Δv = v^p |\nabla v|^q$ in $\mathbb R^n$, which was studied by Bidaut-Véron, García-Huidobro, and Véron. The proof is based on a differential identity and Young inequality. We remark that this is the second version for this paper and the first one was submitted one year ago. We thank Prof. Bidaut-Véron and Véron for their very useful comments on this paper. Compared with the first version, we correct some errors and provide more details for the proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04652 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in $\mathbb R^n$ Ma, Xi-Nan Wu, Wangzhe Analysis of PDEs We improve the Liouville theorem for the equation $-Δv = v^p |\nabla v|^q$ in $\mathbb R^n$, which was studied by Bidaut-Véron, García-Huidobro, and Véron. The proof is based on a differential identity and Young inequality. We remark that this is the second version for this paper and the first one was submitted one year ago. We thank Prof. Bidaut-Véron and Véron for their very useful comments on this paper. Compared with the first version, we correct some errors and provide more details for the proof. |
| title | Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in $\mathbb R^n$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2311.04652 |