Harnack inequalities for quasi-minima of variational integrals
type: Item
instance of: scholarly article
title: Harnack inequalities for quasi-minima of variational integrals
zbMATH Open document ID: 0565.35012
DOI: 10.1016/S0294-1449(16)30424-3
author: Emmanuele DiBenedetto
author: Neil S. Trudinger
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1984-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78076
review text: The main result is that the Harnack inequality can be proved directly for functions in the De Giorgi classes. It is well known that weak solutions of quasilinear elliptic equations, in divergence form, under appropriate structure conditions, belong to De Giorgi classes. Therefore this work provides alternate proofs of the Harnack inequalities for those weak solutions. These results also imply that very non-negative Q-minimum (in the terminology of Giaquinta and Giusti) satisfies a Harnack inequality. The main tools are modifications of the De Giorgi estimates for elliptic equations and a fundamental covering lemma due to Krylov and Safonov.
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 3901241
zbMATH Keywords: quasi-minima
zbMATH Keywords: Harnack inequality
zbMATH Keywords: De Giorgi classes
zbMATH Keywords: quasilinear elliptic equations
zbMATH Keywords: weak solutions
MaRDI profile type: Publication
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OpenAlex ID: W186394053
description: scientific article; zbMATH DE number 3901241