Singular solutions of linear problems with fractional Laplacian
Analysis of PDEs
2019-03-04 v3
Abstract
In this paper, we study singular solutions of linear problems with fractional Laplacian. First, we establish B\^ocher type theorems on a punctured ball via distributional approach. Then, we develop a few interesting maximum principles on a punctured ball. Our distributional approach only requires the basic local L-1 integrability. We also introduce several simple and useful lemmas, which enable us to unify the treatments for both Laplacian and fractional Laplacian. These theorems, lemmas and the methods introduced here can be adapted and applied in other situations.
Cite
@article{arxiv.1801.08232,
title = {Singular solutions of linear problems with fractional Laplacian},
author = {Congming Li and Chenkai Liu and Zhigang Wu and Hao Xu},
journal= {arXiv preprint arXiv:1801.08232},
year = {2019}
}