A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space. (English) Zbl 0837.46025
Summary: Some properties of “concentration-compactness type” are proved to the aim of characterizing the behaviour of bounded sequences of functions in a Sobolev space with respect to Lorentz norms. Such properties are shown to exist as far as the embedding is not optimal with respect to the secundary index.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
Keywords:
concentration-compactness; bounded sequences of functions in a Sobolev space with respect to Lorentz normsReferences:
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