Calculus of Variations and Geometric Measure Theory
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M. Capolli - A. Pinamonti - G. Speight

Maximal Directional Derivatives in Laakso Space

created by pinamonti on 05 Aug 2022

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Inserted: 5 aug 2022
Last Updated: 5 aug 2022

Year: 2022

Abstract:

We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies differentiability only for a $\sigma$-porous set of points. On the other hand, the distance to a fixed point is differentiable everywhere except for a $\sigma$-porous set of points. This behavior is very different to the previously studied settings of Euclidean spaces and Carnot groups.


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