Calculus of Variations and Geometric Measure Theory
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G. E. Comi - V. Magnani

The Gauss-Green theorem in stratified groups

created by magnani on 03 Jun 2018
modified on 21 Feb 2020

[BibTeX]

Published Paper

Inserted: 3 jun 2018
Last Updated: 21 feb 2020

Journal: Adv. Math.
Volume: 360
Number: 106916
Year: 2020
Doi: 10.1016/j.aim.2019.106916

ArXiv: 1806.04011 PDF
Links: postprint

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.

Keywords: Sets of finite perimeter, divergence-measure fields, Gauss-Green theorem, stratified group


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