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

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arxiv 2304.03624 v2 pith:X23DHOYY submitted 2023-04-07 math.AP

Alireza Ataei This is my paper · ORCID
classification math.AP
keywords boundaryfractionallaplaciansolutionsbehaviorboundedcriterioneigenvalue
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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.

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  1. Hopf's lemmas and boundary behaviour of solutions to the fractional Laplacian in Orlicz-Sobolev spaces

    math.AP 2024-11 conditional novelty 6.0 of 10

    Positive weak supersolutions of the fractional a-Laplacian have positive linear boundary growth (a Hopf-type lower bound) under interior ball and growth conditions.

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