带有凸非线性项的分数阶Laplace方程的解的对称性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1224-1234.

带有凸非线性项的分数阶Laplace方程的解的对称性

李振杰^1,^2,*(),李磊²()

¹ 上海交通大学数学科学学院上海 200240
² 南京工业大学数理科学学院南京 211816

收稿日期:2019-01-14 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 李振杰 E-mail:lizhenjie.1113@sjtu.edu.cn;2107430235@qq.com
作者简介:李磊, E-mail:2107430235@qq.com
基金资助:
江苏省自然科学基金(BK20170962)

A Symmetry Result for Solutions of the Fractional Laplacian with Convex Nonlinearites

Zhenjie Li^1,^2,*(),Lei Li²()

¹ School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240
² School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816

Received:2019-01-14 Online:2020-10-26 Published:2020-11-04
Contact: Zhenjie Li E-mail:lizhenjie.1113@sjtu.edu.cn;2107430235@qq.com
Supported by:
the NSF of Jiangsu Province(BK20170962)

摘要/Abstract

摘要：

该文研究了一类带有凸非线性项的分数阶Laplace方程的解的对称性问题，得到：若非线性项关于解严格凸，则该方程在球或环形区域上的Morse指数为1的全局弱解是轴对称的.

关键词: 分数阶Laplace, 极值原理, 分片Schwarz对称

Abstract:

In this paper, we investigate the symmetry property of solutions of the fractional Laplacian with convex nonlinearities. The main result is that all entire weak solutions of the above problem of index 1 on the ball or the annular domain are axially symmetric if the nonlinearity is strictly convex with respect to the solution.

Key words: Fractional Laplacian, Maximum principle, Foliated Schwarz symmetry

中图分类号:

O175.2

李振杰,李磊. 带有凸非线性项的分数阶Laplace方程的解的对称性[J]. 数学物理学报, 2020, 40(5): 1224-1234.

Zhenjie Li,Lei Li. A Symmetry Result for Solutions of the Fractional Laplacian with Convex Nonlinearites[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1224-1234.

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