A Liouville theorem for the higher-order fractional Laplacian

作者：Zhuo, Ran^*; Li, Yan

来源：Communications in Contemporary Mathematics, 2019, 21(2): 1850005.

DOI：10.1142/S0219199718500050

• Higher-order fractional Laplacian
• Green's function
• the method of moving planes
• symmetry
• nonexistence

We study Navier problems involving the higher-order fractional Laplacians. We first obtain nonexistence of positive solutions, known as the Liouville-type theorems, in the upper half-space R-+(n) by studying an equivalent integral form of the fractional equation. Then we show symmetry for positive solutions on B-1(0) through a delicate iteration between lower-order differential/pseudo-differential equations split from the higher-order equation.

• 出版日期2019-3
• 单位黄淮学院