Definitions of Sobolev classes on metric spaces

Bruno Franchi, Piotr Hajłasz, Pekka Koskela

Type: Article

Publication Date: 1999-01-01

Citations: 135

DOI: https://doi.org/10.5802/aif.1742

Abstract

There have been recent attempts to develop the theory of Sobolev spaces W 1,p on metric spaces that do not admit any differentiable structure. We prove that certain definitions are equivalent. We also define the spaces in the limiting case p=1.

Locations

French digital mathematics library (Numdam) - View - PDF
Annales de l’institut Fourier - View - PDF

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