We define a BV-type space in the setting of Carnot groups (i.e., simply connected Lie groups with stratified nilpotent Lie algebra) that allows one to characterize all distributions F for which there exists a continuous horizontal vector field & phi;, vanishing at infinity, that solves the equation divH & phi; = F. This generalizes to the setting of Carnot groups some results by De Pauw and Pfeffer, [13], and by De Pauw and Torres, [14], for the Euclidean setting.

THE DISTRIBUTIONAL DIVERGENCE OF HORIZONTAL VECTOR FIELDS VANISHING AT INFINITY ON CARNOT GROUPS / Baldi, A; Montefalcone, F. - In: LE MATEMATICHE. - ISSN 0373-3505. - STAMPA. - 78:1(2023), pp. 239-271. [10.4418/2023.78.1.9]

THE DISTRIBUTIONAL DIVERGENCE OF HORIZONTAL VECTOR FIELDS VANISHING AT INFINITY ON CARNOT GROUPS

Baldi, A
;
2023

Abstract

We define a BV-type space in the setting of Carnot groups (i.e., simply connected Lie groups with stratified nilpotent Lie algebra) that allows one to characterize all distributions F for which there exists a continuous horizontal vector field & phi;, vanishing at infinity, that solves the equation divH & phi; = F. This generalizes to the setting of Carnot groups some results by De Pauw and Pfeffer, [13], and by De Pauw and Torres, [14], for the Euclidean setting.
2023
THE DISTRIBUTIONAL DIVERGENCE OF HORIZONTAL VECTOR FIELDS VANISHING AT INFINITY ON CARNOT GROUPS / Baldi, A; Montefalcone, F. - In: LE MATEMATICHE. - ISSN 0373-3505. - STAMPA. - 78:1(2023), pp. 239-271. [10.4418/2023.78.1.9]
Baldi, A; Montefalcone, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/939357
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