Retractions onto the space of continuous divergence-free vector fields
type: Item
instance of: scholarly article
title: Retractions onto the space of continuous divergence-free vector fields
zbMATH Open document ID: 1234.47058
author: Philippe Bouafia
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2012-02-18T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/219822
review text: In this paper, it is proved that there does not exist a uniformly continuous retraction from the space of continuous vector fields onto the subspace of vector fields whose divergence vanishes in the distributional sense. The proof relies on the theory of absolutely summing operators and \(\mathcal{L}_{1}\) spaces. In the final section, this result is extended to a more general setting, using the concept of \(m\)-charges due to \textit{T. de Pauw}, \textit{L. Moonens} and \textit{W. F. Pfeffer} [J. Math. Pures Appl. (9) 92, No.~1, 86--112 (2009; Zbl 1166.49039)].
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J99
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 55N35
zbMATH DE Number: 6007122
zbMATH Keywords: vector fields
zbMATH Keywords: \(m\)-charges
reviewed by: Daniel Pellegrino
MaRDI profile type: Publication
OpenAlex ID: W1992061138
cites work: Q5317928
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DOI: 10.5802/AFST.1323
description: scientific article; zbMATH DE number 6007122