2012/10/04 by Lukáš Malý
Mathematics · #Analytic and geometric function theory #Banach space #Differential Equations and Boundary Problems #Function space #Mathematical analysis #Mathematics #Metric space #Nonlinear Partial Differential Equations #Norm (philosophy) #Pointwise #Pure mathematics #Sobolev space #Upper and lower bounds #math.FA #msc:30L99 #msc:46E30 #msc:46E35
paper · pdf · doi:10.5186/aasfm.2013.3831
published as Ann. Acad. Sci. Fenn. Math. 38 (2013), 727-745
arxiv created 2012/10/04 · openalex publication_date 2013/06/01 · arxiv updated 2013/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of particular interest. Existence of minimal weak upper gradients in this general setting is proven and corresponding representation formulae are given. Furthermore, the connection between pointwise convergence of a sequence of Newtonian functions and its convergence in norm is studied.