Differential forms on locally convex spaces and the Stokes formula

TL;DR

This paper extends the Stokes formula to differential forms on locally convex spaces and computes the adjoint of the exterior differential for Sobolev-type forms, broadening the theoretical framework in infinite-dimensional analysis.

Contribution

It introduces a version of the Stokes formula for locally convex spaces and derives the adjoint operator for Sobolev-type differential forms under weaker assumptions.

Findings

Proves a Stokes formula for differential forms on locally convex spaces.

Computes the adjoint of the exterior differential for Sobolev-type forms.

Relates the adjoint to standard calculus operations and the logarithmic derivative.

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.