Calculus of Variations and Geometric Measure Theory

M. Capolli - A. Pinamonti - G. Speight

Maximal Directional Derivatives in Laakso Space

created by pinamonti on 05 Aug 2022
modified on 26 Mar 2024


Accepted Paper

Inserted: 5 aug 2022
Last Updated: 26 mar 2024

Journal: Communications in Contemporary Mathematics
Year: 2022


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.