The Gauss-Green theorem in stratified groups

2018/06/08 by Comi, Giovanni E., Magnani, Valentino · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1806.04011

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.

Cited by

• Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces

Related

• Filling Invariants of Stratified Nilpotent Lie Groups
• The distributional divergence of horizontal vector fields vanishing at infinity on Carnot groups
• Divergence-Measure Fields: Gauss-Green Formulas and Normal Traces
• Beyond BV: new pairings and Gauss-Green formulas for measure fields with divergence measure
• On BV functions and essentially bounded divergence-measure fields in metric spaces