Search results for "Fractional Sobolev spaces"

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Hitchhiker's guide to the fractional Sobolev spaces

2012

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.

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 theoryBull. Sci. Math.
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A quantitative isoperimetric inequality for fractional perimeters

2011

Abstract Recently Frank and Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here in a quantitative form.

Pure mathematicsMathematics::Functional Analysis010102 general mathematicsFractional Sobolev spaces01 natural sciencesFunctional Analysis (math.FA)PerimeterSobolev spaceMathematics - Functional AnalysisQuantitative isoperimetric inequalityMathematics::Group TheoryMathematics - Analysis of PDEs0103 physical sciencesFractional perimeterFOS: MathematicsOrder (group theory)Mathematics::Metric Geometry010307 mathematical physicsMathematics::Differential Geometry0101 mathematicsIsoperimetric inequalityAnalysisMathematicsAnalysis of PDEs (math.AP)
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