# The Gauss--Green theorem in stratified groups

created by magnani on 03 Jun 2018
modified by comi on 07 Sep 2018

[BibTeX]

Preprint

Inserted: 3 jun 2018
Last Updated: 7 sep 2018

Year: 2018

ArXiv: 1806.04011 PDF

Abstract:

We lay the foundations for a theory of divergence-measure fields in noncommutative stratified nilpotent Lie groups. Such vector fields form a new family of function spaces, which generalize in a sense the $BV$ fields. They provide the most general setting to establish Gauss--Green formulas for vector fields of low regularity on sets of finite perimeter. We show several properties of divergence-measure fields in stratified groups, ultimately achieving the related Gauss--Green theorem.