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Generalized rademacher-stepanov type theorem and applications

Ranjbar Motlagh, A ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. Publisher: 2009
  3. Abstract:
  4. The main purpose of this article is to generalize a theorem of Stepanov which provides a necessary and sufficient condition for almost everywhere differentiability of functions over Euclidean spaces. We state and prove an Lp-type generalization of the Stepanov theorem and then we extend it to the context of Orlicz spaces. Then, this generalized Rademacher-Stepanov type theorem is applied to the Sobolev and bounded variation maps with values into a metric space. It is shown that several generalized differentiability type theorems are valid for the Sobolev maps from a Lipschitz manifold into a metric space. As a byproduct, it is shown that the Sobolev spaces of Korevaar-Schoen and Reshetnyak are equivalent. © European Mathematical Society
  5. Keywords:
  6. Generalized differentiability ; Lipschitz manifolds ; Orlicz spaces ; Rademacher and stepanov theorems ; Sobolev and bounded variation spaces
  7. Source: Zeitschrift fur Analysis und ihre Anwendung ; Volume 28, Issue 3 , 2009 , Pages 249-275 ; 02322064 (ISSN)
  8. URL: https://www.ems-ph.org/journals/show_abstract.php?issn=0232-2064&vol=28&iss=3&rank=1