Intrinsic Harnack estimates for singular doubly non-linear equations

Calculus of Variations and Partial Differential Equations 2026 Open access

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Authors: Verena Bögelein, Frank Duzaar, Ugo Gianazza, Naian Liao, Christoph Scheven
DOI: 10.1007/s00526-025-03204-1
Cited by: 2
References: 26

Abstract

Abstract We establish forward, backward and elliptic Harnack inequalities for non-negative solutions to a class of doubly non-linear parabolic partial differential equations. These Harnack estimates are established in a proper range of parameters p and q below. Such a range is shown to be optimal for a Harnack estimate to hold. Quantitative boundedness estimates for solutions and an expansion of positivity result for non-negative super-solutions are instrumental in the proof.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Nonlinear Differential Equations Analysis Advanced Harmonic Analysis Research

Publication details

Journal / source
Calculus of Variations and Partial Differential Equations
Publisher
Springer Science and Business Media LLC
Volume
65
Issue
2
Publication date
12 January 2026
Language
EN