The distributional divergence of horizontal vector fields vanishing at infinity on Carnot groups

2022/10/27 by Baldi, Annalisa, Montefalcone, Francescopaolo
#26D15 #35A23 #35R03 #46E36 #49Q15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2210.15490

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 Φ, vanishing at infinity, that solves the equation divHΦ = F. This generalize to the setting of Carnot groups some results by De Pauw and Pfeffer, [12], and by De Pauw and Torres, [13], for the Euclidean setting.

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