Colombo, MariaTione, Riccardo2022-03-142022-03-142022-03-142022-03-0110.1016/j.matpur.2021.12.005https://infoscience.epfl.ch/handle/20.500.14299/186267WOS:000754667400005In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity condition on the flows themselves. This extends a classical result of Frobenius in the smooth setting. (C) 2021 Elsevier Masson SAS. All rights reserved.Mathematics, AppliedMathematicsregular lagrangian flowscommutativitylie bracketnonsmooth settingordinary differential-equationsdipernatext::journal::journal article::research article