Monday, December 9, 2024 — 12:15 pm — laboratorio Zironi, edificio Matematica
Geometric interpretation of the vanishing Lie Bracket for Sobolev vector fields on the real plane
Abstract: A classical result in differential geometry, ultimately leading to Frobenius theorem, states that the flows of two smooth vector fields $X$, $Y$ commute for all times if and only if their Lie bracket $[X,Y]$ vanishes. In this talk, we consider continuous, Sobolev vector fields with bounded divergence on the real plan, and we discuss an extension of the classical Frobenius theorem in the setting of Regular Lagrangian Flows. 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.
This is a joint project in collaboration with Martina Zizza.