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Differential structure associated to axiomatic Sobolev spaces

2020

The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure. peerReviewed

cotangent moduleLocality of differentialsPure mathematicsGeneral MathematicsAxiomatic Sobolev spaceDifferential structureSpace (mathematics)01 natural sciencesMeasure (mathematics)Settore MAT/05 - Analisi MatematicaFOS: Mathematicsaxiomatic Sobolev space0101 mathematics46E35 51FxxdifferentiaalilaskentaCotangent moduleAxiomMathematicsAxiomatic Sobolev space; Cotangent module; Locality of differentials010102 general mathematicsLocalitymetriset avaruudetFunctional Analysis (math.FA)locality of differentialsSobolev spaceMathematics - Functional AnalysisMetric (mathematics)

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