2014/01/30 by Camille Petit, Petit, Camille, Kai Rajala +3
Mathematics · #46E35 #49J52 #49Q15 #53C65 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:46E35 #msc:49J52 #msc:49Q15 #msc:53C65
paper · pdf · doi:10.48550/arxiv.1401.7956
arxiv created 2014/01/30 · arxiv updated 2014/01/31
A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension m in ℝn with the space of flat m-cochains, that is, the dual space of flat chains of dimension m in ℝn. The main purpose of the present paper is to generalize Wolfe's theorem to the setting of Sobolev differential forms and Sobolev cochains in ℝn. 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.