Liouville theorems for a general class of nonlocal operators

Mouhamed Moustapha Fall; Tobias Weth

Liouville theorems for a general class of nonlocal operators

Analysis of PDEs 2017-10-19 v2

Authors: Mouhamed Moustapha Fall , Tobias Weth

Abstract

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.

Keywords

Liouville theorem nonlocal operators distributional solutions fractional Laplacian partial differential equations anisotropic operators

Cite

@article{arxiv.1504.00419,
  title  = {Liouville theorems for a general class of nonlocal operators},
  author = {Mouhamed Moustapha Fall and Tobias Weth},
  journal= {arXiv preprint arXiv:1504.00419},
  year   = {2017}
}

Comments

some typos were corrected. 15 pages

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