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Spectral Theory and Differential Operators$
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David Edmunds and Des Evans

Print publication date: 2018

Print ISBN-13: 9780198812050

Published to Oxford Scholarship Online: September 2018

DOI: 10.1093/oso/9780198812050.001.0001

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Sobolev Spaces

Sobolev Spaces

(p.203) 5 Sobolev Spaces
Spectral Theory and Differential Operators

D. E. Edmunds

W. D. Evans

Oxford University Press

This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.

Keywords:   embedding, Fourier transform, Poincaré inequality, weak derivative, boundary, extension property, measure of non-compactness

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