Differential forms on locally convex spaces and the Stokes formula

2008/07/14 by Evelina Shamarova, Shamarova, Evelina
Computer Science · Mathematics · #58A10 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #math.FA #msc:58A10

paper · pdf · doi:10.48550/arxiv.0807.2200

openalex publication_date 2008/07/14 · arxiv created 2008/07/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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