A Frobenius-type theorem for singular Lipschitz distributions

TL;DR

This paper proves a Frobenius-type theorem for singular Lipschitz distributions generated by vector fields that meet a finite type condition almost everywhere, advancing the understanding of integrability in nonsmooth contexts.

Contribution

It establishes a Frobenius-type integrability theorem for singular Lipschitz distributions under a finite type condition, extending classical results to nonsmooth settings.

Findings

Proves a Frobenius-type theorem for singular Lipschitz distributions.

Shows integrability under a finite type condition almost everywhere.

Extends classical Frobenius theorem to nonsmooth vector fields.

Abstract

We prove a Frobenius-type theorem for singular distributions generated by a family of locally Lipschitz continuous vector fields satisfying almost everywhere a quantitative finite type condition.