Calculus of Variations and Geometric Measure Theory

G. E. Comi - G. Crasta - V. De Cicco - A. Malusa

Representation formulas for pairings between divergence-measure fields and $BV$ functions

created by comi on 23 Aug 2022
modified on 16 Oct 2023


Published Paper

Inserted: 23 aug 2022
Last Updated: 16 oct 2023

Journal: Journal of Functional Analysis
Year: 2023
Doi: 10.1016/j.jfa.2023.110192


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 In particular, we extend a representation formula from an unpublished paper of Anzellotti involving the limit of cylindrical averages for normal traces, and we exploit a result of Šilhavý in order to derive another representation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.

Keywords: Gauss-Green formula, divergence-measure fields, normal traces