Geometric interpretation of the vanishing Lie Bracket for two-dimensional rough vector fields
| Autor: | Rebucci, Annalaura, Zizza, Martina |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we prove that if $X,Y$ are continuous, Sobolev vector fields with bounded divergence on the real plane and $[X,Y]=0$, then their flows commute. In particular, we improve the previous result of Colombo-Tione (2021), where the authors require the additional assumption of the weak Lie differentiability on one of the two flows. We also discuss possible extensions to the $\text{BV}$ setting. |
| Databáze: | arXiv |
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