Topology of Sobolev mappings III

✍ Scribed by Fengbo Hang; Fanghua Lin

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 357 KB
• Volume: 56
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/cpa.10098

✦ Synopsis

Abstract

We establish a necessary and sufficient topological condition for maps that are in W^1,p^(M, N) to be connected by continuous paths in W^1,p^(M, N) to maps in W^1,q^(M, N), q > q ≥ 1. We also obtain a necessary and sufficient topological condition under which W^1,q^(M, N) is strongly dense in W^1,p^(M, N). Several results concerning sequential weak density of smooth (or W^1,q^(M, N) maps in W^1,p^(M, N) are also proven. © 2003 Wiley Periodicals, Inc.