6533b828fe1ef96bd1287c00

RESEARCH PRODUCT

Hitchhiker's guide to the fractional Sobolev spaces

Giampiero PalatucciGiampiero PalatucciEnrico ValdinociEnrico ValdinociEleonora Di Nezza

subject

Pure mathematicsMathematics(all)General MathematicsMathematical proof01 natural sciencesSobolev inequalityFractional LaplacianSobolev embeddingsMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaFOS: Mathematics0101 mathematicsNehari manifoldMathematicsSobolev spaces for planar domains010102 general mathematicsMathematical analysisFractional Sobolev spacesFractional Sobolev spaces; Gagliardo norm; Fractional Laplacian; Nonlocal energy; Sobolev embeddingsGagliardo normNonlocal energyFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsSobolev spaceInterpolation spaceAnalysis of PDEs (math.AP)CounterexampleTrace theory

description

AbstractThis paper deals with the fractional Sobolev spaces Ws,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.

yearjournalcountryeditionlanguage
2012-07-01Bull. Sci. Math.
10.1016/j.bulsci.2011.12.004http://dx.doi.org/10.1016/j.bulsci.2011.12.004