Some Liouville theorems for the fractional Laplacian

Wenxiong Chen, Lorenzo D'Ambrosio, Yan Li

In this paper, we prove the following result. Let $\alpha$ be any real number between $0$ and $2$. Assume that $u$ is a solution of $$ \left\{\begin{array}{ll} (-Δ)^{α/2} u(x) = 0 , \;\…