J. Korean Math. Soc. 2018; 55(6): 1423-1433
Online first article March 21, 2018 Printed November 1, 2018
https://doi.org/10.4134/JKMS.j170724
Copyright © The Korean Mathematical Society.
Yayun Li, Bei Liu
Nanjing Normal University, Nanjing Normal University
This paper is concerned about several quasilinear elliptic systems with $m$-Laplacians. According to the Liouville theorems of those systems on $\mathbb R^n$, we obtain the singularity estimates of the positive $C^1$-weak solutions on bounded or unbounded domain (but it is not $\mathbb R^n$) and their decay rates on the exterior domain when $|x| \to \infty$. The doubling lemma which is developed by Polacik-Quittner-Souplet plays a key role in this paper. In addition, the corresponding results of several special examples are presented.
Keywords: elliptic system of $m$-Laplacian, doubling lemma, Liouville theorem, singularity estimate, decay rate
MSC numbers: 35B40, 35J47, 35J92
2021; 58(6): 1327-1345
1996; 33(2): 455-468
1999; 36(1): 73-95
2002; 39(5): 731-743
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd