A Harnack inequality for fractional Laplace equations with lower order terms

TL;DR

This paper proves a Harnack inequality for fractional Laplace equations with lower order terms, using Moser's iteration and John-Nirenberg inequality, without requiring sign conditions on the zero order coefficient.

Contribution

It introduces a new approach to establish Harnack inequalities for fractional Laplace equations without sign restrictions on lower order coefficients.

Findings

Established a Harnack inequality for fractional Laplace equations

Applied Moser's iteration and John-Nirenberg inequality in the proof

Removed sign condition constraints on the zero order term

Abstract

We establish a Harnack inequality of fractional Laplace equations without imposing sign condition on the coefficient of zero order term via the Moser's iteration and John-Nirenberg inequality.