Regularity results for differential forms solving degenerate elliptic systems
type: Item
instance of: scholarly article
title: Regularity results for differential forms solving degenerate elliptic systems
zbMATH Open document ID: 1266.35052
author: Lisa Beck
author: Bianca Stroffolini
published in: Calculus of Variations and Partial Differential Equations
publication date: 2013-03-18T00:00:00Z
review text: This paper deals with the regularity of weak solutions for some classes of degenerate elliptic problems on bounded domains. In the first part, the authors are concerned with a possible degeneracy at the origin like the \(p\)-Laplace or even systems of Uhlenbeck structure. The main tools in the proofs are the \(p\)-harmonic approximation lemma and the \(a\)-approximation method. Next, the authors present a unified and simplified proof of the partial regularity result for the sub- and the superquadratic case. The theoretical arguments developed in this paper could also serve to deal with other regularity issues for differential forms, such as partial regularity (and dimension reduction for the singular set) in the context of parabolic systems or Calderon-Zygmund-type estimates with nonstandard growth.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35J48
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6145938
zbMATH Keywords: regularity of solutions
zbMATH Keywords: differential form
zbMATH Keywords: degenerate elliptic system
MaRDI profile type: Publication
full work available at URL: s00526-012-0503-6
OpenAlex ID: W2145046302
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DOI: 10.1007/S00526-012-0503-6
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description: scientific article; zbMATH DE number 6145938