Harnack inequality for quasilinear elliptic equations in generalized Orlicz-Sobolev spaces
type: Item
instance of: scholarly article
title: Harnack inequality for quasilinear elliptic equations in generalized Orlicz-Sobolev spaces
zbMATH Open document ID: 1445.35099
author: Allami Benyaiche
author: Ismail Khlifi
published in: Potential Analysis
publication date: 2020-07-20T00:00:00Z
review text: The authors prove the Harnack inequality for positive solutions of quasilinear elliptic equations in the generalized Orlicz-Sobolev space setting. Their approach is based on the usage of the upper envelope function \(G^+\) of a \(\Phi\)-function \(G(\cdot)\) and the Moser's iteration technique. Assuming a structure condition on \(G(\cdot)\) and a Harnack condition introduced by \textit{P. Harjulehto} et al. [Calc. Var. Partial Differ. Equ. 56, No. 2, Paper No. 22, 26 p. (2017; Zbl 1366.35036)], they get the Hölder continuity of bounded solutions. We recall that such regularity result was proved in previuos papers but using completely different approaches.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 31C45
zbMATH DE Number: 7223214
zbMATH Keywords: generalized Orlicz-Sobolev spaces
zbMATH Keywords: \( \Phi \)-functions
zbMATH Keywords: Harnack inequality
zbMATH Keywords: Hölder continuity
MaRDI profile type: Publication
full work available at URL: s11118-019-09781-z
OpenAlex ID: W2942716592
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Wikidata QID: Q127928661
DOI: 10.1007/S11118-019-09781-Z
description: scientific article; zbMATH DE number 7223214