Data di Pubblicazione:
2012
Citazione:
Hitchhiker's guide to the fractional Sobolev spaces / E. Di Nezza, G. Palatucci, E. Valdinoci. - In: BULLETIN DES SCIENCES MATHEMATIQUES. - ISSN 0007-4497. - 136:5(2012), pp. 521-573. [10.1016/j.bulsci.2011.12.004]
Abstract:
This paper deals with the fractional Sobolev spaces Ws,pWs,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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Fractional Sobolev spaces; Gagliardo norm; Fractional Laplacian; Nonlocal energy; Sobolev embeddings
Elenco autori:
E. Di Nezza, G. Palatucci, E. Valdinoci
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