A Liouville Theorem for the Fractional Laplacian
Analysis of PDEs
2014-01-30 v1
Abstract
We extend the classical Liouville Theorem from Laplacian to the fractional Laplacian, that is, we prove Every -harmonic function bounded either above or below in all of must be constant.
Keywords
Cite
@article{arxiv.1401.7402,
title = {A Liouville Theorem for the Fractional Laplacian},
author = {Ran Zhuo and Wenxiong Chen and Xuewei Cui and Zixia Yuan},
journal= {arXiv preprint arXiv:1401.7402},
year = {2014}
}
Comments
14 pages