Calculus of Variations and Geometric Measure Theory
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E. Le Donne - A. Pinamonti - G. Speight

Universal differentiability sets and maximal directional derivatives in Carnot groups

created by speight on 16 May 2017

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Inserted: 16 may 2017
Last Updated: 16 may 2017

Year: 2017

Abstract:

We show that every Carnot group G of step 2 admits a Hausdorff dimension one `universal differentiability set' N such that every real-valued Lipschitz map on G is Pansu differentiable at a point of N. This relies on the fact that existence of a maximal directional derivative of f at a point x implies Pansu differentiability at the same point x. We show that such an implication holds in Carnot groups of step 2 but fails in the Engel group which has step 3.


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