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

Domenico Mucci

Journal of the European Mathematical Society (2001)

  • Volume: 003, Issue: 1, page 1-38
  • ISSN: 1435-9855

Abstract

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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.

How to cite

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Mucci, Domenico. "A characterization of graphs which can be approximated in area by smooth graphs." Journal of the European Mathematical Society 003.1 (2001): 1-38. <http://eudml.org/doc/277312>.

@article{Mucci2001,
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 $n\ge 3$ 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.},
author = {Mucci, Domenico},
journal = {Journal of the European Mathematical Society},
keywords = {vector valued map; weak convergence; approximation by smooth maps; Cartesian currents; approximation in area; currents},
language = {eng},
number = {1},
pages = {1-38},
publisher = {European Mathematical Society Publishing House},
title = {A characterization of graphs which can be approximated in area by smooth graphs},
url = {http://eudml.org/doc/277312},
volume = {003},
year = {2001},
}

TY - JOUR
AU - Mucci, Domenico
TI - A characterization of graphs which can be approximated in area by smooth graphs
JO - Journal of the European Mathematical Society
PY - 2001
PB - European Mathematical Society Publishing House
VL - 003
IS - 1
SP - 1
EP - 38
AB - 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 $n\ge 3$ 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.
LA - eng
KW - vector valued map; weak convergence; approximation by smooth maps; Cartesian currents; approximation in area; currents
UR - http://eudml.org/doc/277312
ER -

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