An elementary partial regularity proof for vector-valued obstacle problems
type: Item
instance of: scholarly article
title: An elementary partial regularity proof for vector-valued obstacle problems
zbMATH Open document ID: 0609.35011
DOI: 10.1007/BF01461719
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164318
review text: We analyze the partial regularity properties of vector-valued Sobolev- functions u which minimize energy-type functionals under a non-convex side-condition of the form Im(u)\(\subset \bar M\) for a bounded smooth domain M in the image space. Although our results are not new, the method outlined here simplifies and unifies the various techniques developed by F. Duzaar and the author (see the references quoted in the paper). The approach presented here is based on a rather elementary blow-up lemma and an extension-theorem for maps defined on spheres with values in \=M to the whole ball. Combining these facts we get an energy-decay estimate near points with small energy. Moreover, the same technique applies to the related p-harmonic obstacle problem for exponents \(p>2\), which could not be handled with our former techniques.
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 3985731
zbMATH Keywords: partial regularity
zbMATH Keywords: Sobolev-functions
zbMATH Keywords: energy-type functionals
zbMATH Keywords: non- convex side-condition
zbMATH Keywords: blow-up
zbMATH Keywords: extension
zbMATH Keywords: energy-decay estimate
zbMATH Keywords: points with small energy
zbMATH Keywords: p-harmonic obstacle problem
author: M. Fuchs
MaRDI profile type: Publication
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OpenAlex ID: W1983375137
description: scientific article; zbMATH DE number 3985731