Harnack's inequality for quasilinear elliptic equations with singular absorption term
type: Item
instance of: scholarly article
title: Harnack's inequality for quasilinear elliptic equations with singular absorption term
zbMATH Open document ID: 1415.35065
published in: Potential Analysis
publication date: 2019-04-30T00:00:00Z
review text: In this interesting paper, the author is concerned with divergence type quasilinear elliptic equations with measurable coefficients and singular lower order term. More precisely, the author studies Harnack inequality of nonnegative solutions to the equations \[ -\operatorname{div}A(x, \nabla u) + a_0(x, u) = b(x, \nabla u),\quad x \in \Omega, \] where $\Omega$ is a domain in $\mathbb{R}^n$, $n \geq 2$, $A$ is an operator with a $p$-Laplacean structure, $a_0$ is a lower term and $b$ is an absorption term with singular coefficients. To treat the quasilinear case of $p$-Laplacian with a lower order term, Biroli introduced the notion of the nonlinear Kato class. His method was extended to more general cases by using the Kilpelainen-Maly technique. In this paper the author extends these results to the case of elliptic equations with absorption term. The difficulty is that neither De Giorgi nor Moser iteration techniques work in this situation. In this paper, by using the Kilpelainen-Maly technique, the author establishes the Harnack inequality for the $p$-Laplace equation perturbed by absorbtion term with singular coefficient.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35J92
zbMATH DE Number: 7049464
zbMATH Keywords: divergence type quasilinear elliptic equations
zbMATH Keywords: measurable coefficients
zbMATH Keywords: singular lower order term
zbMATH Keywords: nonlinear Kato class
zbMATH Keywords: Kilpelainen-Maly technique
author: Igor I. Skrypnik
MaRDI profile type: Publication
full work available at URL: s11118-018-9691-9
OpenAlex ID: W2795429914
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DOI: 10.1007/S11118-018-9691-9
description: scientific article; zbMATH DE number 7049464