Doubling measures, Poincar\'e inequalities and parabolic Harnack inequalities for a doubly nonlinear equation
Analysis of PDEs
2026-05-28 v1
Abstract
We characterize metric measure spaces satisfying parabolic Harnack inequalities for a doubly nonlinear equation in terms of volume doubling and Poincar\'e 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.
Keywords
Cite
@article{arxiv.2605.27665,
title = {Doubling measures, Poincar\'e inequalities and parabolic Harnack inequalities for a doubly nonlinear equation},
author = {Theo Elenius and Juha Kinnunen},
journal= {arXiv preprint arXiv:2605.27665},
year = {2026}
}