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Lack of compactness in the 2D critical Sobolev embedding, the general case

✍ Scribed by Bahouri, Hajer; Majdoub, Mohamed; Masmoudi, Nader

Book ID
120392475
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
666 KB
Volume
101
Category
Article
ISSN
0021-7824

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Let (u n ) be a bounded sequence in H s, p (R d ) (0<s<d p). We show that (u n ) has a subsequence (u$ n ) such that each u$ n can be expressed as a finite sum (plus a remainder) of translationsÂdilations of functions , m and such that the remainder has arbitrary small norm in L q (1Âq=(1Âp)&(sÂd )