Frobenius-type theorems for Lipschitz distributions (Q2464471)

The main aim of the paper is to present a Frobenius type theorem for distributions on manifolds which are only Lipschitz. The main result is Theorem 4.11 which presents 13 equivalent conditions which are satisfied by integrable Lipschitz distributions, and which are expressed in the language of Lipschitz vector fields and 1-forms. In the preceding sections the author presents the classical \(C^2\) integrability conditions in detail and with clarity discusses possible generalizations which could be valid and useful in the Lipschitz case. These considerations lead to the formulation of the Frobenius theorem for Lipschitz distributions. Its proof is presented in the last section of the paper. It is an interesting paper which can help to develop the theory of Lipschitz foliations with applications in geometric control theory.