On Some Aspects of the Theory of Orlicz–Sobolev Spaces

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


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.


Sobolev Space Lipschitz Domain Orlicz Space Equivalent Norm Lorentz Space 
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© 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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