Doubling measures, Poincaré inequalities and parabolic Harnack inequalities for a doubly nonlinear equation

Abstract

We characterize metric measure spaces satisfying parabolic Harnack inequalities for a doubly nonlinear equation in terms of volume doubling and Poincaré inequalities. Our approach uses purely analytical methods, based on obtaining estimates for solutions to a related Cauchy problem. This extends previous linear results to the nonlinear setting without relying on heat kernel estimates and representation formulae.