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A decomposition theorem for BV functions

Stefano Bianchini 1 Daniela Tonon 2
2 C&O - Equipe combinatoire et optimisation
IMJ-PRG - Institut de Mathématiques de Jussieu - Paris Rive Gauche
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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Submitted on : Wednesday, August 22, 2012 - 5:56:16 PM
Last modification on : Tuesday, December 8, 2020 - 3:36:58 AM

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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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