Harnack inequality for the nonlocal equations with general growth

TL;DR

This paper establishes a version of Harnack inequalities for generalized nonlocal p-Laplacian equations, expanding understanding of weak solutions through structural conditions, positivity, and energy estimates.

Contribution

It introduces structural conditions enabling Harnack inequalities for nonlocal equations with general growth, advancing theoretical understanding.

Findings

Derived nonlocal Harnack inequalities for weak solutions

Identified structural conditions for inequalities to hold

Used expansion of positivity and energy estimates

Abstract

We consider a class of generalized nonlocal $p$-Laplacian equations. We find some proper structural conditions to establish a version of nonlocal Harnack inequalities of weak solutions to such nonlocal problems by using the expansion of positivity and energy estimates.