9

Gauss-Green theorem

The classical Gauss–Green theorem on open sets with *C*^{1}-boundary plays a fundamental role in the theory of sets of finite perimeter. We shall build its proof on a nice application of the area formula to codimension one graphs (Section 9.1), and then generalize it to the case of open sets whose boundaries fail to be of class *C*^{1} due to the presence of an *H*^{n–1}-negligible set (Section 9.3). **Throughout this chapter we use Notation 4.**

**9.1 Area of a graph of codimension one**

Given *u* : ^{n–1} → and *G* ⊂ ^{n–1}, we define the **graph of** *u*

Start Free Trial

No credit card required