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

Journal of the European Mathematical Society (2001)

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

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topMucci, 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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