Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SINGULARITY ESTIMATES FOR ELLIPTIC SYSTEMS OF m-LAPLACIANS

  • Li, Yayun (Institute of Mathematics School of Mathematical Sciences Nanjing Normal University) ;
  • Liu, Bei (School of Mathematical Sciences Nanjing Normal University)
  • Received : 2017.11.09
  • Accepted : 2018.02.27
  • Published : 2018.11.01
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Abstract

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 ${\mid}x{\mid}{\rightarrow}{\infty}$. 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.

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References

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