Frobenius-type theorems for Lipschitz distributions

Abstract

We generalize the classical Frobenius Theorem to distributions that are spanned by locally Lipschitz vector fields. The various versions of the involutivity conditions are extended by means of set-valued Lie derivatives-in particular, set-valued Lie brackets-and set-valued exterior derivatives. A PDEs counterpart of these Frobenius-type results is investigated as well. © 2007 Elsevier Inc. All rights reserved.