Liouville theorems for a general class of nonlocal operators

Mouhamed Moustapha Fall, Tobias Weth

Published 2015-04-02Version 1

In this paper, we study the equation $\mathcal{L} u=0$ in $\mathbb{R}^N$, where $\mathcal{L}$ belongs to a general class of nonlocal linear operators which may be anisotropic and nonsymmetric. We classify distributional solutions of this equation, thereby extending and generalizing recent Liouville type theorems in the case where $\mathcal{L}= (-\Delta)^s$, $s \in (0,1)$ is the classical fractional Laplacian.