A priori gradient bounds and local \(C^{1,\alpha}\)-estimates for (double) obstacle problems under non-standard growth conditions
type: Item
instance of: scholarly article
title: A priori gradient bounds and local \(C^{1,\alpha}\)-estimates for (double) obstacle problems under non-standard growth conditions
zbMATH Open document ID: 1011.49024
DOI: 10.4171/ZAA/1054
author: M. Bildhauer
author: M. Fuchs
author: Giuseppe Mingione
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2003-05-21T00:00:00Z
review text: The paper deals with local gradient bounds and interior Hölder regularity for the first derivatives of functions \(u\in W^{1,1}_{\text{ loc}}(\Omega)\) which minimize locally the variational integral \[ \int_\Omega f(\nabla u)dx \] and are subject to the side condition \(\Psi_1\leq u\leq \Psi_2\) almost everywhere in a bounded domain \(\Omega\subset {\mathbb R}^n,\) \(n\geq 2.\) The function \(f\colon {\mathbb R}^n\to [0,\infty)\) is a strictly convex one and satisfies suitable non-standard growth conditions as \(|Z|\to\infty.\) In particular, these include the case of \(f(Z)=|Z|^p\log (1+|Z|),\) its iterated version and also integrands of \((p,q)\)-growth.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 35J85
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1747399
zbMATH Keywords: a priori estimates
zbMATH Keywords: regularity of minimizers
zbMATH Keywords: double obstacle problem
zbMATH Keywords: non-standard growth
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/1054
OpenAlex ID: W2007681780
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description: scientific article; zbMATH DE number 1747399