2015/01/31 by Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen · 1 citation
Mathematics · #Analytic and geometric function theory #Bounded function #Combinatorics #Geometric Analysis and Curvature Flows #Geometry #Integer (computer science) #Lipschitz continuity #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Product (mathematics) #Pure mathematics #Riemannian manifold #Sobolev space #math.FA #msc:46E35 #msc:46T20 #msc:58D15
paper · pdf · doi:10.1007/s10231-017-0664-1
published as Ann. Mat. Pura Appl. (4) 196 (2017), no. 6, 2261-2301 · Accepted for publication in Annali di Matematica Pura ed Applicata (1923 -)
openalex publication_date 2017/05/04 · arxiv created 2017/05/08 · arxiv updated 2018/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Given a complete noncompact Riemannian manifold Nn, we investigate whether the set of bounded Sobolev maps (W1, p ∩ L^∞) (Qm; Nn) on the cube Qm is strongly dense in the Sobolev space W1, p (Qm; Nn) for 1 ≤ p ≤ m. The density always holds when p is not an integer. When p is an integer, the density can fail, and we prove that a quantitative trimming property is equivalent with the density. This new condition is ensured for example by a uniform Lipschitz geometry of Nn. As a byproduct, we give necessary and sufficient conditions for the strong density of the set of smooth maps C^∞ (Qm; Nn) in W1, p (Qm; Nn).