On the uniqueness of solutions of a nonlocal elliptic system

被引：18
作者：
Wang, Kelei [1 ,2 ]
Wei, Juncheng [3 ,4 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
[2] Wuhan Univ, Computat Sci Hubei Key Lab, Wuhan 430072, Peoples R China
[3] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
[4] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
来源：
MATHEMATISCHE ANNALEN | 2016年 / 365卷 / 1-2期
基金：
加拿大自然科学与工程研究理事会;
关键词：
MODELING PHASE-SEPARATION; FRACTIONAL DIFFUSION; STRONG COMPETITION; SEGREGATION; REGULARITY; EQUATIONS;
D O I：
10.1007/s00208-015-1271-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the following elliptic system with fractional Laplacian -(-Delta)(s)u = uv(2), -(-Delta)(s) v = vu(2), u, v > 0 on R-n, where s is an element of (0, 1) and (-Delta)(s) is the s-Lapalcian. We first prove that all positive solutions must have polynomial bound. Then we use the Almgren monotonicity formula to perform a blown- down analysis. Finally we use the method of moving planes to prove the uniqueness of the one dimensional profile, up to translation and scaling.
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页码：105 / 153
页数：49
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