A Liouville Theorem for the Higher Order Fractional Laplacian
Analysis of PDEs
2018-02-07 v1
Abstract
We deal with the higher-order fractional Laplacians by two methods: the integral method and the system method. The former depends on the integral equation equivalent to the differential equation. The latter works directly on the differential equations. We first derive nonexistence of positive solutions, often known as the Liouville type theorem, for the integral and differential equations. Then through an delicate iteration, we show symmetry for positive solutions.
Keywords
Cite
@article{arxiv.1609.04105,
title = {A Liouville Theorem for the Higher Order Fractional Laplacian},
author = {Ran Zhuo and Yan Li},
journal= {arXiv preprint arXiv:1609.04105},
year = {2018}
}