# A Frobenius-type theorem for singular Lipschitz distributions

@article{Montanari2011AFT,
title={A Frobenius-type theorem for singular Lipschitz distributions},
author={Annamaria Montanari and Daniele Morbidelli},
journal={Journal of Mathematical Analysis and Applications},
year={2011},
volume={399},
pages={692-700}
}
• Published 20 October 2011
• Mathematics
• Journal of Mathematical Analysis and Applications
11 Citations
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## References

SHOWING 1-10 OF 26 REFERENCES

. We show that if a distribution is locally spanned by Lipschitz vector (cid:12)elds and is involutive a.e., then it is uniquely integrable giving rise to a Lipschitz foliation with leaves of class C
• Mathematics
• 2006
We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the subbundle S defines
We study multi-parameter Carnot-Caratheodory balls, generalizing results due to Nagel, Stein, and Wainger in the single parameter setting. The main technical result is seen as a uniform version of
• Mathematics
• 2013
We consider a family ${\mathcal{H}}:= \{X_1, \dots, X_m\}$ of C1 vector fields in ℝn and we discuss the associated ${\mathcal{H}}$-orbits. Namely, we assume that our vector fields belong to a
Summary. A smooth distribution on a smooth manifold M is, by definition, a map that assigns to each point x of M a linear subspace Δ(x) of the tangent space T x M, in such a way that, locally, there
A smooth distribution on a smooth manifold M is, by definition, a map that assigns to each point x of M a linear subspace ∆(x) of the tangent space TxM , in such a way that, locally, there exist
Let D be an arbitrary set of Cc vector fields on the Cc manifold M. It is shown that the orbits of D are C' submanifolds of M, and that, moreover, they are the maximal integral submanifolds of a