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Sharp Differentiability Results for the Lower Local Lipschitz Constant and Applications to Non-embedding

Wildrick, K. ; Zürcher, T.

In: The Journal of Geometric Analysis, 2015, vol. 25, no. 4, p. 2590-2616

The Stepanov differentiability theorem in metric measure spaces

Balogh, Zoltán ; Rogovin, Kevin ; Zürcher, Thomas

In: The Journal of Geometric Analysis, 2004, vol. 14, no. 3, p. 405-422

Sharp differentiability results for the lower local Lipschitz constant and applications to non-embedding

Wildrick, Kevin ; Zürcher, Thomas

In: The Journal of Geometric Analysis, 2015, vol. 25, no. 4, p. 2590–2616

We give a sharp condition on the lower local Lipschitz constant of a mapping from a metric space supporting a Poincaré inequality to a Banach space with the Radon–Nikodym property that guarantees differentiability at almost every point. We apply these results to obtain a non-embedding theorem for a corresponding class of mappings.