Liouville theorem for quasilinear elliptic equations in $\mathbb R^N$

Wangzhe Wu; Qiqi Zhang

Liouville theorem for quasilinear elliptic equations in $\mathbb R^N$

Analysis of PDEs 2023-11-23 v1

Authors: Wangzhe Wu , Qiqi Zhang

Abstract

We prove Liouville theorem for the equation $\Delta_m v + v^p + M |\nabla v|^{q}= 0$ in a domain $\Omega\subset\mathbb R^n$ , with $M\in \mathbb{R}$ in the critical and subcritical case. As a natural extension of our recent work \cite{MWZ}, the proof is based on an integral identity and Young's inequality.

Keywords

liouville theorem quasilinear elliptic equations integral identity young's inequality critical case subcritical case

Cite

@article{arxiv.2311.13418,
  title  = {Liouville theorem for quasilinear elliptic equations in $\mathbb R^N$},
  author = {Wangzhe Wu and Qiqi Zhang},
  journal= {arXiv preprint arXiv:2311.13418},
  year   = {2023}
}

Related papers

View all related →