Calculus of Variations and Geometric Measure Theory

G. Crasta - V. De Cicco

Anzellotti's pairing theory and the Gauss-Green theorem

created by decicco on 02 Aug 2017
modified on 05 Dec 2018


Accepted Paper

Inserted: 2 aug 2017
Last Updated: 5 dec 2018

Journal: Advances in Mathematics
Year: 2018


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 the Anzellotti's pairing theory and by characterizing the measure pairing (A, Du) when A is a bounded divergence measure vector field and u is a bounded function of bounded variation.