LOCAL BEHAVIOR OF SOLUTIONS TO A FRACTIONAL EQUATION WITH ISOLATED SINGULARITY AND CRITICAL SERRIN EXPONENT

被引：2

作者：

Wei, Juncheng ^{[1
]}

Wu, Ke ^{[2
]}

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2022年 / 42卷 / 08期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Serrin exponent; isolated singularity; local behavior; Caffarelli-Silvestre extension; removable singularity; SEMILINEAR ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; ASYMPTOTICS; EXISTENCE;

D O I：

10.3934/dcds.2022044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the local behavior of positive singular solutions to the equation (-Delta)(sigma) u = u(n/n-2 sigma )in B-1\{0} where (-Delta)(sigma) is the fractional Laplacian operator, 0 < sigma < 1 and n/n-2 sigma the critical Serrin exponent. We show that either u can be extended as a continuous function near the origin or there exist two positive constants c(1) and c(2) such that c(1)vertical bar x vertical bar(2 sigma-n)(- ln vertical bar x vertical bar) - (n - 2 sigma/2 sigma) <= u(x) <= c(2)vertical bar x vertical bar)(-2 sigma-n )(-ln vertical bar x vertical bar)(-n-2 sigma/2 sigma) in B-1\{0}.

引用

页码：4031 / 4050

页数：20

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