A comparison method for the fractional Laplacian and applications
Alireza Ataei, Alireza Tavakoli · Advances in Mathematics · 2024
We study the boundary behavior of solutions to fractional Laplacian. 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 Laplacian.