单位球上分数阶Laplace方程正解的径向对称性与单调性  

Radial Symmetry and Monotonicity of the Fractional Laplacian Equation in the Unit Ball

作　　者：窦美霞[1] 李静[1] 

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《河南师范大学学报（自然科学版）》2016年第4期1-6,共6页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11271111)

摘　　要：首先研究单位球上分数阶Laplace方程分布意义下的解与其对应的积分方程等价,然后,基于微分方程与积分方程的等价性,对积分方程运用积分形式的移动平面法证明正解的径向对称性与单调性,从而得到分数阶Laplace方程正解的径向对称性与单调性.This paper investigates radial symmetry and monotonicity of the fractional Laplacian equation in the unit ball Firstly, we show the equivalence between the differential equation and the integral equation. Based on the equivalence, we prove the radial symmetry and monotonicity by using the moving planes approach to the integral equation, and we also get the radial symmetry and monotonicity of the fractional Laplacian equation.

关 键 词：分数阶Laplacian算子 积分形式的移动平面法 径向对称性 单调性 

分 类 号：O175.5[理学—数学]