A decomposition theorem for BV functions

Stefano Bianchini 1 Daniela Tonon 2
2 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
Abstract : The Jordan decomposition states that a function is of bounded variation if and only if it can be written as the difference of two monotone increasing functions. In this paper we generalize this property to real valued functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa. A counterexample is given which prevents further extensions.
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Article dans une revue
Communications on Pure and Applied Mathematics, Wiley, 2011, 10 (6), pp.1549 - 1566. 〈10.3934/cpaa.2011.10.1549〉
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Soumis le : mercredi 22 août 2012 - 17:56:16
Dernière modification le : mercredi 21 mars 2018 - 18:57:28

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Stefano Bianchini, Daniela Tonon. A decomposition theorem for BV functions. Communications on Pure and Applied Mathematics, Wiley, 2011, 10 (6), pp.1549 - 1566. 〈10.3934/cpaa.2011.10.1549〉. 〈hal-00724835〉

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