A comparison method for the fractional Laplacian and applications
Analysis of PDEs
2023-04-03 v2
Abstract
We study the boundary behavior of solutions to fractional elliptic equations. As the first result, the isolation of the first eigenvalue of the fractional Lane-Emden equation is proved in the bounded open sets with Wiener regular boundary. Then, a generalized Hopf's lemma and a global boundary Harnack inequality are proved for the fractional elliptic equations.
Cite
@article{arxiv.2302.06262,
title = {A comparison method for the fractional Laplacian and applications},
author = {Alireza Ataei and Alireza Tavakoli},
journal= {arXiv preprint arXiv:2302.06262},
year = {2023}
}
Comments
20 pages, several minor corrections