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On Some Aspects of the Theory of Orlicz–Sobolev Spaces

  • Andrea Cianchi
Chapter
Part of the International Mathematical Series book series (IMAT, volume 11)

Abstract

We survey results, obtained by the author and his coauthors over the last fifteen years, on optimal Sobolev embeddings and related inequalities in Orlicz spaces. Some of the presented results are very recent and are not published yet. We recall basic properties concerning Orlicz and Orlicz–Sobolev spaces and then dicsuss embeddings of Sobolev type and embeddings into spaces of uniformly continuous functions, classical and approximate differentiability properties of Orlicz–Sobolev functions and also trace inequalities on the boundary.

Keywords

Sobolev Space Lipschitz Domain Orlicz Space Equivalent Norm Lorentz Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Applicazioni per l’ArchitetturaUniversità di FirenzeFirenzeItaly

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