Harnack's inequality for doubly nonlinear equations of slow diffusion type
type: Item
instance of: scholarly article
title: Harnack's inequality for doubly nonlinear equations of slow diffusion type
zbMATH Open document ID: 1473.35075
author: Verena Bögelein
author: Andreas Herán
author: Leah Schätzler
author: Thomas Singer
published in: Calculus of Variations and Partial Differential Equations
publication date: 2021-09-06T00:00:00Z
review text: In this article the authors prove a Harnack inequality for non-negative weak solutions to doubly nonlinear parabolic equations of the form \[\partial_t u- \operatorname{div} A(x, t, u, Du^m) = \operatorname{div} F,\] where the vector field \(A\) fulfills p-ellipticity and growth conditions. The authors treat the slow diffusion case in its full range, i.e. all exponents \(m > 0\) and \(p > 1\) with \(m(p- 1) > 1\) are included. Till now, some cases (for instance \(m(p - 1) > 1\) and \(1<p<2\)) were never considered. Lastly, the authors introduce a definition of weak solution involving \(u^m\), which is new even for the doubly degenerate case and the slow diffusion porous medium equation.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 7391399
zbMATH Keywords: doubly degenerate equations
zbMATH Keywords: slow diffusion case
zbMATH Keywords: Harnack inequalities
MaRDI profile type: Publication
full work available at URL: s00526-021-02044-z
OpenAlex ID: W3197717696
Wikidata QID: Q115386508
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DOI: 10.1007/S00526-021-02044-Z
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description: scientific article; zbMATH DE number 7391399