Journal of the
Korean Mathematical Society JKMS

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