Inserted: 23 aug 2022
Last Updated: 16 oct 2023
Journal: Journal of Functional Analysis
The purpose of this paper is to find pointwise representation formulas for the density of the pairing between divergence-measure fields and BV functions, in this way continuing the research started in Anzellotti's pairing theory and Pairings between bounded divergence-measure vector fields and $BV$ functions. In particular, we extend a representation formula from an unpublished paper of Anzellotti involving the limit of cylindrical averages for normal traces, and we exploit a result of Šilhavý in order to derive another representation in terms of limits of averages in half balls.