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.

Hitchhikerʼs guide to the fractional Sobolev spaces / Eleonora Di Nezza; Giampiero Palatucci; Enrico Valdinoci. - In: BULLETIN DES SCIENCES MATHEMATIQUES. - ISSN 0007-4497. - 136:5(2012), pp. 521-573. [10.1016/j.bulsci.2011.12.004]

Hitchhikerʼs guide to the fractional Sobolev spaces

PALATUCCI, Giampiero;
2012

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2688488
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