2015/01/31 by Lior Falach, Reuven Segev · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Domain (mathematical analysis) #Embedding #Euclidean space #Lipschitz continuity #Mathematical analysis #Mathematics #Measure (data warehouse) #Norm (philosophy) #Numerical methods in inverse problems #Open set #Pure mathematics #math-ph #math.MP
paper · pdf · doi:10.1007/s00161-015-0461-2
27 pages
arxiv created 2015/01/31 · openalex publication_date 2015/07/28 · arxiv updated 2016/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A generalized transport theorem for convecting irregular domains is presented in the setting of Federer's geometric measure theory. A prototypical r-dimensional domain is viewed as a flat r-chain of finite mass in an open set of an n-dimensional Euclidean space. The evolution of such a generalized domain in time is assumed to be in accordance to a bi-Lipschitz type map. The induced curve is shown to be continuous with respect to the flat norm and differential with respect to the sharp norm on currents in ℝn. A time dependent property is naturally assigned to the evolving region via the action of an r-cochain on the current associated with the domain. Applying a representation theorem for cochains the properties are shown to be locally represented by an r-form. Using these notions a generalized transport theorem is presented.