The distributional divergence of horizontal vector fields vanishing at infinity on Carnot groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915318583001088 |
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| author | Baldi, Annalisa Montefalcone, Francescopaolo |
| author_facet | Baldi, Annalisa Montefalcone, Francescopaolo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15490 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The distributional divergence of horizontal vector fields vanishing at infinity on Carnot groups Baldi, Annalisa Montefalcone, Francescopaolo Functional Analysis 35A23, 35R03, 26D15, 46E36, 49Q15 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. |
| title | The distributional divergence of horizontal vector fields vanishing at infinity on Carnot groups |
| topic | Functional Analysis 35A23, 35R03, 26D15, 46E36, 49Q15 |
| url | https://arxiv.org/abs/2210.15490 |