Keller-Osserman a priori estimates and the Harnack inequality for the evolution \(p\)-Laplace equation with singular absorption term
type: Item
instance of: scholarly article
title: Keller-Osserman a priori estimates and the Harnack inequality for the evolution \(p\)-Laplace equation with singular absorption term
zbMATH Open document ID: 1400.35042
author: Igor I. Skrypnik
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-08-27T00:00:00Z
review text: In this paper, the author studies quasilinear equations of type \[ u_t-\operatorname{div}(|\nabla u| ^{p-2}\nabla u)+V(x)f(u)=0, \] where \(p\geq 2\) and \(u \geq 0\). Starting from the original ideas due to DiBenedetto-Gianazza-Vespri, many authors proved intrinsic Harnack estimates for evolution \(p\)-Laplace type equations with lower order terms from Kato classes and with absorption term. In this paper, the author makes a first attempt to study the Harnack inequality for degenerate quasilinear parabolic equations perturbed by singular absorption term. Despite the lack of comparison principle, he proves a priori estimates of Keller-Osserman type, and using these estimates he shows that a suitable intrinsic Harnack inequality holds.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K92
zbMATH DE Number: 6925394
zbMATH Keywords: large solutions
zbMATH Keywords: quasilinear parabolic equations
zbMATH Keywords: singular absorption term
zbMATH Keywords: lack of comparison principle
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.07.046
OpenAlex ID: W2884022423
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DOI: 10.1016/J.JMAA.2018.07.046
description: scientific article; zbMATH DE number 6925394