Boundary behavior of solutions to fractional $p$-Laplacian equation

Alireza Ataei

Boundary behavior of solutions to fractional $p$-Laplacian equation

Analysis of PDEs 2025-02-24 v2

Authors: Alireza Ataei

Abstract

In this work, a generalized Hopf's lemma and a global boundary Harnack inequality are proved for solutions to fractional $p$ -Laplacian equations. Then, the isolation of the first $(s,p)$ -eigenvalue is shown in bounded open sets satisfying the Wiener criterion.

Keywords

fractional p-Laplacian Hopf lemma boundary Harnack inequality Wiener criterion eigenvalue isolation

Cite

@article{arxiv.2304.03624,
  title  = {Boundary behavior of solutions to fractional $p$-Laplacian equation},
  author = {Alireza Ataei},
  journal= {arXiv preprint arXiv:2304.03624},
  year   = {2025}
}

Comments

There have been some major corrections to Section 5 and some more clarifications and minor typos in other sections

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