An extension of the pairing theory between divergence-measure fields and BV functions

TL;DR

This paper introduces a nonlinear extension of Anzellotti's pairing between divergence-measure fields and BV functions, leading to a generalized Gauss-Green formula with potential applications in evolutionary quasilinear problems.

Contribution

It develops a nonlinear pairing concept and proves a generalized Gauss-Green formula, expanding the theoretical framework for divergence-measure fields and BV functions.

Findings

Established a nonlinear pairing between divergence-measure fields and BV functions.

Proved a generalized Gauss-Green formula for the new pairing.

Potential applications to evolutionary quasilinear problems.

Abstract

In this paper we introduce a nonlinear version of the notion of Anzellotti's pairing between divergence--measure vector fields and functions of bounded variation, motivated by possible applications to evolutionary quasilinear problems. As a consequence of our analysis, we prove a generalized Gauss--Green formula.