Frobenius-type theorems for Lipschitz distributions

[摘要] 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. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] distribution;involutivity;integral manifold;Lipschitz tensor field;set-valued tensor field