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arXiv · 2605.27665

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

Theo Elenius·Juha Kinnunen
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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.

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Theo Elenius, Juha Kinnunen. 2026-05-26. Doubling measures, Poincaré inequalities and parabolic Harnack inequalities for a doubly nonlinear equation. https://arxiv.org/abs/2605.27665

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