Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (5): 1224-1234.

Previous Articles     Next Articles

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

Zhenjie Li1,2,*(),Lei Li2()   

  1. 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)

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

CLC Number: 

  • O175.2
Trendmd