Leaf superposition property for integer rectifiable currents

2008, Volume 3, Issue 1: 85-95. doi: 10.3934/nhm.2008.3.85

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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

We consider the class of integer rectifiable currents without boundary in $\R^n\times\R$ 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.
- Integer rectifiable currents,
- Cartesian currents,
- Currents in metric spaces,
- Metric spaces valued $BV$ functions,
- Multi-valued functions
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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Abstract

We consider the class of integer rectifiable currents without boundary in $\R^n\times\R$ 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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