Consider the Sobolev class W s, p (M, N ) where M and N are compact manifolds, and p β₯ 1, s β (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 β W s,
Fractional order Sobolev spaces on Wiener space
β Scribed by Shinzo Watanabe
- Publisher
- Springer
- Year
- 1993
- Tongue
- English
- Weight
- 1015 KB
- Volume
- 95
- Category
- Article
- ISSN
- 1432-2064
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## Abstract The best constant and extremal functions for Sobolev trace inequalities on fractional Sobolev spaces are achieved by a simple argument. Β© 2011 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim
Taking lim sup L Γ lim k Γ in both sides of (2.10), by (i), (2.8), (2.9), and the fact that lim k Γ \* k =1 we get a contradiction. Hence, , is not identically zero.
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