Petit, Camille Rajala, Kai Wenger, Stefan 2015-04-15 A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension <em>m  </em> in RⁿRn with the space of flat <em>m</em>-cochains, that is, the dual space of flat chains of dimension <em>m  </em> in RⁿRn. The main purpose of the present paper is to generalize Wolfe's theorem to the setting of Sobolev differential forms and Sobolev cochains in RⁿRn. 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. application/pdf https://folia.unifr.ch/global/documents/304392 https://folia.unifr.ch/documents/304392/files/wer_wtw.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2015.01.006 info:eu-repo/semantics/openAccess License undefined Journal of Functional Analysis. - 2015, vol. 268, no. 8, p. 2261–2297 Weakly differentiable cochain Polyhedral chain Flat cochain Geometric integration theory info:eu-repo/classification/udc/53 Wolfe’s theorem for weakly differentiable cochains http://purl.org/coar/resource_type/c_6501