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Fractional Sobolev spaces and topology

✍ Scribed by Pierre Bousquet

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 446 KB
Volume: 68
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2006.11.038

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✦ Synopsis

Consider the Sobolev class W s, p (M, N ) where M and N are compact manifolds, and p ≥ 1, s ∈ (0, 1 + 1/ p). We present a necessary and sufficient condition for two maps u and v in W s, p (M, N ) to be continuously connected in W s, p (M, N ). We also discuss the problem of connecting a map u ∈ W s, p (M, N ) to a smooth map f ∈ C ∞ (M, N ).

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## 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 condi