An Anzellotti type pairing for divergence-measure fields and a notion of weakly super-$1$-harmonic functions

Abstract

We study generalized products of divergence-measure fields and gradient measures of {\rm BV} functions. These products depend on the choice of a representative of the {\rm BV} function, and here we single out a specific choice which is suitable in order to define and investigate a notion of weak supersolutions for the $1$-Laplace operator.