Harnack’s inequality for nonlocal parabolic equations

Naian Liao (University of Salzburg)

Abstract: Harnack’s inequality asserts that the ratio of two values of positive harmonic functions over a compact set is bounded. A Harnack-type inequality for positive solutions to the heat equation was independently formulated by Hadamard and Pini in 1954. A crucial character is the so-called waiting-time phenomenon. A decade later Moser showed a deep result that the Harnack inequality continued to hold for solutions to parabolic equations with bounded and measurable coefficients. I will introduce recent advances on Harnack’s inequality for nonlocal parabolic equations.