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Universal differentiability sets and maximal directional derivatives in Carnot groups. (arXiv:1705.05871v1 [math.FA])
来源于:arXiv
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. 查看全文>>