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Wolfe's theorem for weakly differentiable cochains

Kai RajalaCamille PetitStefan Wenger

subject

Mathematics - Differential GeometryPure mathematicsDifferential form49Q15 46E35 53C65 49J52Mathematics::Algebraic Topology01 natural sciencesMathematics - Analysis of PDEs0103 physical sciencesFOS: MathematicsDifferentiable function0101 mathematicsflat cochainMathematicsFundamental theoremDual spaceta111polyhedral chain010102 general mathematicsCohomologySobolev spaceDifferential Geometry (math.DG)Norm (mathematics)010307 mathematical physicsgeometric integration theoryweakly differentiable cochainAnalysisAnalysis of PDEs (math.AP)

description

Abstract A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension m in R n with the space of flat m -cochains, that is, the dual space of flat chains of dimension m in R n . The main purpose of the present paper is to generalize Wolfe's theorem to the setting of Sobolev differential forms and Sobolev cochains in R n . A suitable theory of Sobolev cochains has recently been initiated by the second and third author. It is based on the concept of upper norm and upper gradient of a cochain, introduced in analogy with Heinonen–Koskela's concept of upper gradient of a function.

yearjournalcountryeditionlanguage
2014-01-30
http://arxiv.org/abs/1401.7956