Intrinsic geometry and De Giorgi classes for certain anisotropic problems
type: Item
instance of: scholarly article
title: Intrinsic geometry and De Giorgi classes for certain anisotropic problems
zbMATH Open document ID: 1370.35140
author: P. Baroni
author: Agnese Di Castro
author: Giampiero Palatucci
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2017-05-03T00:00:00Z
review text: The authors deal with nonlinear operators and functional classes modeled after the anisotropic Laplacian operator. We recall that anisotropic operators appear especially in Physics, when directional derivatives with distinct weights create distortions in the ambient space. The authors give a natural extension of the usual De Giorgi classes for functions in the anisotropic Sobolev spaces based on the intrinsic (parabolic) scaling proposed by DiBenedetto. Moreover, they prove that the anisotropic De Giorgi classes contain the quasi-minima \(u\) of any energy anisotropic functional.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6710660
zbMATH Keywords: anisotropic Laplacian operator
zbMATH Keywords: anisotropic Sobolev spaces
zbMATH Keywords: anisotropic De Giorgi classes
MaRDI profile type: Publication
full work available at URL: dcdss.2017032
OpenAlex ID: W2605987980
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DOI: 10.3934/DCDSS.2017032
description: scientific article; zbMATH DE number 6710660