Harnack inequality and an asymptotic mean-value property for the Finsler infinity-Laplacian
type: Item
instance of: scholarly article
title: Harnack inequality and an asymptotic mean-value property for the Finsler infinity-Laplacian
zbMATH Open document ID: 1469.35009
author: Benyam Mebrate
author: Ahmed Mohammed
publication date: 2021-07-05T00:00:00Z
review text: The study of anisotropic problems in calculus of variations goes all the way back to at least the seminal work by George Wullf who studied the mathematical theory of crystals and minimization of surface energies. Closely related to this is the anisotropic Laplacian (or Finsler Laplacian). The Finsler-Minkowski norms lead to natural generalizations of many classical elliptic operators, and this has motivated the study of elliptic operators defined with respect to Finsler-Minkowski norms. In this paper, the authors prove a Harnack inequality for nonnegative viscosity supersolutions of nonhomogeneous equations associated with normalized Finsler infinity-Laplace operators. Viscosity solutions to homogeneous equations are also characterized via an asymptotic mean-value property, understood in a viscosity sense.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35A23
Mathematics Subject Classification ID: 35D40
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 7367617
zbMATH Keywords: Finsler-Minkowski norm
zbMATH Keywords: Harnack inequality
zbMATH Keywords: asymptotic mean-value property
zbMATH Keywords: nonnegative viscosity supersolutions
Wikidata QID: Q114053240
MaRDI profile type: Publication
full work available at URL: acv-2018-0083
OpenAlex ID: W2968159580
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DOI: 10.1515/ACV-2018-0083
published in: Advances in the Calculus of Variations
description: scientific article; zbMATH DE number 7367617