Wolfe’s theorem for weakly differentiable cochains

Petit, Camille; Rajala, Kai; Wenger, Stefan

doi:10.1016/j.jfa.2015.01.006

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Journal article

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

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