2011/01/02 by Jenny Harrison, Harrison, Jenny
Computer Science · Mathematics · #46E99 #49Q15 #58C99 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #math.FA #msc:46E99 #msc:49Q15 #msc:58C99
paper · pdf · doi:10.48550/arxiv.1101.0979
59 pages, 15 figures
openalex publication_date 2011/01/02 · arxiv created 2012/03/04 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a topological predual to differential forms constructed as an inductive limit of a sequence of Banach spaces. This subspace of currents has nice properties, in that Dirac chains and polyhedral chains are dense, and its operator algebra contains operators predual to exterior derivative, Hodge star, Lie derivative, and interior product. Using these operators, we establish higher order divergence theorems for net flux of k-vector fields across nonsmooth boundaries, Stokes' theorem for domains in open sets which are not necessarily regular, and a new fundamental theorem for nonsmooth domains and their boundaries moving in a smooth flow. We close with broad generalizations of the Leibniz integral rule and Reynold's transport theorem.