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A characterization of graphs which can be approximated in area by smooth graphs

A characterization of graphs which can be approximated in area by smooth graphs For vector valued maps, convergence in W 1,1 and of all minors of the Jacobian matrix in L 1 is equivalent to convergence weakly in the sense of currents and in area for graphs. We show that maps defined on domains of dimension n≥ 3 can be approximated strongly in this sense by smooth maps if and only if the same property holds for the restriction to a.e. 2-dimensional plane intersecting the domain. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

A characterization of graphs which can be approximated in area by smooth graphs

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References (27)

Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Berlin Heidelberg & EMS
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/PL00011301
Publisher site
See Article on Publisher Site

Abstract

For vector valued maps, convergence in W 1,1 and of all minors of the Jacobian matrix in L 1 is equivalent to convergence weakly in the sense of currents and in area for graphs. We show that maps defined on domains of dimension n≥ 3 can be approximated strongly in this sense by smooth maps if and only if the same property holds for the restriction to a.e. 2-dimensional plane intersecting the domain.

Journal

Journal of the European Mathematical Society – Springer Journals

Published: Feb 1, 2001

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