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arXiv · 2208.03361

Maximal Directional Derivatives in Laakso Space

Marco Capolli·Andrea Pinamonti·Gareth Speight
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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 completely different to the previously studied settings of Euclidean spaces and Carnot groups.

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Marco Capolli, Andrea Pinamonti, Gareth Speight. 2022-08-05. Maximal Directional Derivatives in Laakso Space. https://arxiv.org/abs/2208.03361

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