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Article Dans Une Revue Communications on Pure and Applied Mathematics Année : 2011

A decomposition theorem for BV functions

Daniela Tonon
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Résumé

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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Dates et versions

hal-00724835 , version 1 (22-08-2012)

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Citer

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