A theorem on improving regularity of minimizing sequences by reverse Hölder inequalities
type: Item
instance of: scholarly article
title: A theorem on improving regularity of minimizing sequences by reverse Hölder inequalities
zbMATH Open document ID: 0894.49023
author: Baisheng Yan
author: Zhengfang Zhou
published in: Michigan Mathematical Journal
publication date: 1998-08-19T00:00:00Z
review text: Let \(M^{n\times m}\) denote the space of all real \(n\times m\)-matrices and consider a closed subset \(K\) of \(M^{n\times m}\) which satisfies \[ d_k(\lambda X)\leq k_0(d_k(X)+ 1) \] for all \(X\in M^{n\times m}\) and \(0\leq\lambda\leq 1\). Here \(k_0\) is some positive constant and \(d_k(\cdot)\) is the distance function of the set \(K\). On the Sobolev space \(W^1_p(D,\mathbb{R}^n)\), \(D\subset\mathbb{R}^m\), the author now introduces the energy \[ I_p(u, D)= \int_D d^p_k(\nabla u)dx, \] and shows that any weakly convergent minimizing sequence from \(W^1_p(D,\mathbb{R}^n)\) can be replaced by a minimizing sequence with higher integrability and better convergence properties. This result has applications in the theory of weakly almost conformal mappings.
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 1127771
zbMATH Keywords: reverse Hölder inequalities
zbMATH Keywords: minimizing sequences
zbMATH Keywords: regularity
reviewed by: M. Fuchs
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029005787
OpenAlex ID: W2010756684
DOI: 10.1307/MMJ/1029005787
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description: scientific article; zbMATH DE number 1127771