Anzellotti's pairing theory and the Gauss–Green theorem.

Abstract In this paper we obtain a very general Gauss–Green formula for weakly differentiable functions and sets of finite perimeter. This result is obtained by revisiting Anzellotti's pairing theory and by characterizing the measure pairing (A , D u) when A is a bounded divergence measure vector field and u is a bounded function of bounded variation. [ABSTRACT FROM AUTHOR]