Hitchhiker's guide to the fractional Sobolev spaces

Details Hitchhiker's guide to the fractional Sobolev spaces Hitchhiker's guide to the fractional Sobolev spaces

2011-04-21

arxiv.org/abs/1104.4345v3

Mathematics

Functional Analysis

Scientific paper

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.

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