For vector valued maps, convergence in W1,1 and of all minors of the Jacobian matrix in L1 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.

A characterization of graphs which can be approximated in area by smooth graphs / MUCCI D.. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 3(2001), pp. 1-38. [10.1007/s100970000025]

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

MUCCI, Domenico
2001

Abstract

For vector valued maps, convergence in W1,1 and of all minors of the Jacobian matrix in L1 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.
A characterization of graphs which can be approximated in area by smooth graphs / MUCCI D.. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 3(2001), pp. 1-38. [10.1007/s100970000025]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/1456090
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact