Nonlocal Harnack inequalities

TL;DR

This paper establishes a general Harnack inequality for minimizers of nonlocal integro-differential operators, including the fractional p-Laplacian, extending classical results to a broader nonlocal and possibly degenerate setting.

Contribution

It introduces a new general Harnack inequality applicable to nonlocal, possibly degenerate operators like the fractional p-Laplacian, advancing the theoretical understanding of such operators.

Findings

Proves a general Harnack inequality for nonlocal minimizers

Extends classical inequalities to fractional p-Laplacian

Provides a framework for degenerate nonlocal operators

Abstract

We state and prove a general Harnack inequality for minimizers of nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian.