Wolfe’s theorem for weakly differentiable cochains
- Petit, Camille University of Jyväskylä, Department of Mathematics and Statistics, University of Jyväskylä, Finland
- Rajala, Kai University of Jyväskylä, Department of Mathematics and Statistics, University of Jyväskylä, Finland
- Wenger, Stefan Université de Fribourg, Mathématiques, Switzerland
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15.04.2015
Published in:
- Journal of Functional Analysis. - 2015, vol. 268, no. 8, p. 2261–2297
English
A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension m in RⁿRn with the space of flat m-cochains, that is, the dual space of flat chains of dimension m 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.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Physics
- License
- License undefined
- Identifiers
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- RERO DOC 255974
- DOI 10.1016/j.jfa.2015.01.006
- Persistent URL
- https://folia.unifr.ch/unifr/documents/304392
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