Inserted: 3 jun 2018
Last Updated: 14 jan 2020
Journal: Adv. Math.
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.
Keywords: Sets of finite perimeter, divergence-measure fields, Gauss-Green theorem, stratified group