On the uniqueness of solutions of a nonlocal elliptic system

被引：19

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.

引用

页码：105 / 153

页数：49

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