SYMMETRY OF POSITIVE SOLUTIONS FOR EQUATIONS INVOLVING HIGHER ORDER FRACTIONAL LAPLACIAN

被引：7
作者：
Li, Yan [1 ]
Zhuo, Ran [1 ,2 ]
机构：
[1] Yeshiva Univ, Dept Math Sci, New York, NY 10033 USA
[2] Huanghuai Univ, Dept Math Sci, Zhumadian 463000, Henan, Peoples R China
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 10期
关键词：
Higher order fractional Laplacian; fractional Laplacian; the method of moving planes; rotational symmetry; equivalence; LIOUVILLE TYPE THEOREMS; OBSTACLE PROBLEM; REGULARITY; SYSTEM; CLASSIFICATION; DIFFUSION; BOUNDARY;
D O I：
10.1090/proc/13052
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider problems associated with the higher order fractional Laplacian. Through the method of moving planes, we derive rotational symmetry of positive solutions and show their dependence on the x(n) variable only. We also establish the equivalence between a semilinear higher order fractional Laplacian equation and its corresponding integral equation, so as to further deduce a Liouville type theorem and obtain a priori estimates for positive solutions.
引用
收藏
页码：4303 / 4318
页数：16
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