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
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Main Authors: Ma, Xi-Nan, Wu, Wangzhe
Format: Preprint
Published: 2023
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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