Journal
BULLETIN DES SCIENCES MATHEMATIQUES
Volume 136, Issue 5, Pages 521-573Publisher
ELSEVIER
DOI: 10.1016/j.bulsci.2011.12.004
Keywords
Fractional Sobolev spaces; Gagliardo norm; Fractional Laplacian; Nonlocal energy; Sobolev embeddings
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Funding
- Istituto Nazionale di Alta Matematica F. Seven (Indam)
- ERC grant Vectorial problems [207573]
- ERC grant epsilon Elliptic Pde's and Symmetry of Interfaces and Layers for Odd Nonlinearities
- FIRB project A&B Analysis and Beyond
- European Research Council (ERC) [207573] Funding Source: European Research Council (ERC)
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This paper deals with the fractional Sobolev spaces W-s,W-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. (c) 2011 Elsevier Masson SAS. All rights reserved.
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