Calculus of Variations and Geometric Measure Theory
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Z. Balogh - K. Rogovin - T. Zürcher

The Stepanov differentiability theorem in metric measure spaces

created on 06 Apr 2004
modified by zoltan on 08 Dec 2004

[BibTeX]

Published Paper

Inserted: 6 apr 2004
Last Updated: 8 dec 2004

Journal: Journal of Geometric Analysis
Volume: 14
Number: 3
Pages: 405-422
Year: 2004

Abstract:

We extend Cheeger's theorem on differentiability of Lipschitz functions in metric measure spaces to the class of functions satisfying Stepanov's condition. As consequence, we obtain the analogue of Calderon's differentiability theorem of Sobolev functions in metric measure spaces satisfying a Poincaré inequality.

Keywords: Stepanov differentiability , doubling measure, differentiable structure, Poincare inequality

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