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Networks and Heterogeneous Media

2008, Volume 3, Issue 1: 85-95. doi: 10.3934/nhm.2008.3.85
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Leaf superposition property for integer rectifiable currents

  • 1.
    Scuola Normale Superiore, p.za dei Cavalieri 7, Pisa, I-56126
  • 2.
    Dipartimento di Matematica, Università degli Studi di Parma, viale G.P. Usberti 53/A (Campus), 43100 Parma
  • 3.
    Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris
  • Received: 01 June 2007 Revised: 01 September 2007

  • Primary: 49Q15; Secondary: 26B30, 30C55.

  • We consider the class of integer rectifiable currents without boundary in \Rn×\R satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.

    Citation: Luigi Ambrosio, Gianluca Crippa, Philippe G. Lefloch. Leaf superposition property for integer rectifiable currents[J]. Networks and Heterogeneous Media, 2008, 3(1): 85-95. doi: 10.3934/nhm.2008.3.85

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  • We consider the class of integer rectifiable currents without boundary in \Rn×\R satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.


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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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