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 08 Jun 2018



Inserted: 3 jun 2018
Last Updated: 8 jun 2018

Year: 2018


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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