A decomposition theorem for BV functions

Stefano Bianchini (1) , Daniela Tonon (1)

1 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies

The Jordan decomposition states that a real valued function of one variable 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 BV 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.

Domaines: Equations aux dérivées partielles [math.AP]

Stefano Bianchini, Daniela Tonon. A decomposition theorem for BV functions. Communications on Pure and Applied Analysis, 2011, 10 (6), pp.1549-1566. ⟨hal-00918429⟩