Topology of Sobolev Mappings III

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We establish a necessary and sufficient topological condition for maps that are in W1,p (M, N) to be connected by continuous paths in W 1,p (M, N) to maps in W1,q (M, N), q > p ≥ 1. We also obtain a necessary and sufficient topological condition under which W 1,q (M, N) is strongly dense in W1,p (M, N). Several results concerning sequential weak density of smooth (or W1,q (M, N)) maps in W1,p (M, N) are also proven.

Original languageEnglish (US)
Pages (from-to)1383-1415
Number of pages33
JournalCommunications on Pure and Applied Mathematics
Issue number10
StatePublished - Oct 2003

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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