The Gauss-Green theorem in stratified groups

Giovanni E. Comi; Valentino Magnani

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arXiv · 1806.04011

The Gauss-Green theorem in stratified groups

Giovanni E. Comi·Valentino Magnani

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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.

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Giovanni E. Comi, Valentino Magnani. 2018-06-08. The Gauss-Green theorem in stratified groups. https://arxiv.org/abs/1806.04011

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