Hitchhiker's guide to the fractional Sobolev spaces

Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

2113 Citations (Web of Science)


This paper deals with the fractional Sobolev spaces W s,p. We analyze the relations among some of their possible definitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results. Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains.

Original languageEnglish
Pages (from-to)521-573
Number of pages53
JournalBulletin des Sciences Mathematiques
Issue number5
Publication statusPublished - 1 Jul 2012
Externally publishedYes


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