2023/07/12 by Camillo Brena, Nicola Gigli, Brena, Camillo +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.2307.06008
openalex publication_date 2023/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an alternative proof of the general chain rule for functions of bounded variation ([ADM90]), which allows to compute the distributional differential of φ∘ F, where φ∈ LIP(ℝm) and F\inBV(ℝn,ℝm). In our argument we build on top of recently established links between `closability of certain differentiation operators' and `differentiability of Lipschitz functions in related directions' ([ABM23]): we couple this with the observation that `the map that takes φ and returns the distributional differential of φ∘ F is closable' to conclude. Unlike previous results in this direction, our proof can directly be adapted to the non-smooth setting of finite dimensional RCD spaces.