Time-insensitive nonlocal parabolic Harnack estimates

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.

to appear in Proc. Lond. Math. Soc