Two dimensional variational problems with linear growth
type: Item
instance of: scholarly article
title: Two dimensional variational problems with linear growth
zbMATH Open document ID: 1026.49028
author: M. Bildhauer
published in: Manuscripta Mathematica
publication date: 2003-07-02T00:00:00Z
review text: Consider the variational functional with the integrand \(f \in C^{2}(\mathbb{R}^{nN}) \) of linear growth : \[ J(u)= \int _{\Omega} f( Du(x)) dx. \] and the generalized minimizers in the class \(u\in u_{0}+ W_{0}^{1,1}\), defined as the functions \(u\in \text{BV}\) which is the \(L^{1}\)-limit of some \(J\)-minimizing sequences \((u_{k}) \in u_{0}+ W_{0}^{1,1}\). Under some structure conditions, and \(f(z)=g(|z|)\) in the vectorial case \(N>1\), the author generalizes some previous results showing that when \(n=2\), the restriction \(u_{0}\in L^\infty \) is superfluous to obtain that the generalized minimizers are in \(C^{1,\alpha}\) .
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 49M29
Mathematics Subject Classification ID: 35J45
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 74G65
Mathematics Subject Classification ID: 49J10
zbMATH DE Number: 1945278
zbMATH Keywords: variational functional
zbMATH Keywords: generalized minimizers
reviewed by: Elvira Mascolo
MaRDI profile type: Publication
full work available at URL: s00229-002-0338-0
OpenAlex ID: W4252519268
DOI: 10.22028/D291-26206
DOI: 10.1007/S00229-002-0338-0
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description: scientific article; zbMATH DE number 1945278