Time-insensitive nonlocal parabolic Harnack estimates

TL;DR

This paper introduces novel Harnack estimates for nonlocal parabolic equations that do not require waiting time for global solutions, expanding understanding of solution behavior with general operators.

Contribution

It presents new Harnack estimates that eliminate waiting-time constraints for global solutions and demonstrates the necessity of waiting-time for local solutions in nonlocal parabolic equations.

Findings

New Harnack estimates for global solutions without waiting-time

Waiting-time is necessary for local solutions in nonlocal parabolic equations

Applicable to general nonlocal operators with measurable coefficients

Abstract

We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal operators with bounded measurable coefficients. Moreover, we show that a waiting-time is required for the nonlocal parabolic Harnack inequality when local solutions are considered.