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Analysis of the Lack of Compactness in the Critical Sobolev Embeddings

✍ Scribed by Stéphane Jaffard

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
128 KB
Volume
161
Category
Article
ISSN
0022-1236

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✦ Synopsis

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 )). This generalizes a result obtained by Patrick Ge rard for the case p=2.

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