Differential forms on locally convex spaces and the Stokes formula

Abstract

We prove a version of the Stokes formula for differential forms on locally convex spaces. The main tool used for proving this formula is the surface layer theorem proved in another paper by the author. Moreover, for differential forms of a Sobolev-type class relative to a differentiable measure, we compute the operator adjoint to the exterior differential in terms of standard operations of calculus of differential forms and the logarithmic derivative. Previously, this connection was established under essentially stronger assumptions.