2013/10/30 by Behroz Bidabad, Bidabad, Behroz, Alireza Shahi +1 · 1 citation
Mathematics · Physics and Astronomy · #46E35 #53C60 #Advanced Differential Geometry Research #Boundary (topology) #Boundary value problem #Compact space #Differential Geometry (math.DG) #Dirichlet distribution #Domain (mathematical analysis) #Extension (predicate logic) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Sobolev inequality #Sobolev space #Space (punctuation) #math.DG #msc:46E35 #msc:53C60
paper · pdf · doi:10.48550/arxiv.1310.8027
13 pages
arxiv created 2013/10/30 · openalex publication_date 2013/10/30 · arxiv updated 2013/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (M,F) be a C^∞ Finsler manifold, p≥ 1 a real number, k a positive integer and Hkp (M) a certain Sobolev space determined by a Finsler structure F. Here, it is shown that the set of all real C∞ functions with compact support on M is dense in the Sobolev space H1p (M). This result permits to approximate certain solution of Dirichlet problem living on H1p (M) by C^ ∞ functions with compact support on (M,F). Moreover, let W ⊂ M be a regular domain with the Cr boundary ∂ W, then the set of all real functions in Cr (W) ∩ C0 ( W) is dense in Hkp (W), where k≤ r. This work is an extension of some density theorems of T. Aubin on Riemannian manifolds.