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. (C) 2019 Elsevier Inc. All rights reserved.
Comi, G., Magnani, V. (2020). The Gauss–Green theorem in stratified groups. ADVANCES IN MATHEMATICS, 360, 1-85 [10.1016/j.aim.2019.106916].
The Gauss–Green theorem in stratified groups
Comi, G. E.;
2020
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. (C) 2019 Elsevier Inc. All rights reserved.| File | Dimensione | Formato | |
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