Topology of Sobolev Mappings III

Fengbo Hang; Fanghua Lin

doi:10.1002/cpa.10098

Topology of Sobolev Mappings III

Fengbo Hang, Fanghua Lin

Mathematics

Research output: Contribution to journal › Article › peer-review

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 > p ≥ 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.

Original language	English (US)
Pages (from-to)	1383-1415
Number of pages	33
Journal	Communications on Pure and Applied Mathematics
Volume	56
Issue number	10
DOIs	https://doi.org/10.1002/cpa.10098
State	Published - Oct 2003

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.10098

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AB - 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.

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Topology of Sobolev Mappings III

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