Differentiation on a lipschitz manifold

Abstract

In a smooth manifold with corners, a corner is a singular point. In the more general family of Lipschitz manifolds, a corner is no more singular.

The differentiation operator ▽;Γ being defined for a Lipschitz manifold, it has no singularity at the possible corners of a manifold.

So, some calculus on smooth (or C¹) manifolds may be extended to the case of manifoldswith corners.

This is done here for the expansion of an integral on Γ. Similar results may be done for the expansion of physical quantities defined via boundary value problems such as the drag of a body. More generally the differential calculus on manifolds with corners may be useful in a lot of problems.

It remains to give the full proves, which require a full book.