scholarly journals Universal extension for Sobolev spaces of differential forms and applications

2012 ◽  
Vol 263 (2) ◽  
pp. 364-382 ◽  
Author(s):  
Ralf Hiptmair ◽  
Jingzhi Li ◽  
Jun Zou
Keyword(s):  
Sobolev Spaces ◽  
Differential Forms ◽  
Universal Extension

Sobolev Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Sobolev Spaces ◽  
Embedding Theorems ◽  
Approximation Numbers ◽  
Selection Of

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.

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