Universal differentiability sets and maximal directional derivatives in Carnot groups
Abstract
We show that every Carnot group G of step 2 admits a Hausdorff dimension one ‘universal differentiability set’ N such that every Lipschitz map f : G → R is Pansu differentiable at some 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.
Main Authors
Format
Articles
Research article
Published
2019
Series
Subjects
Publication in research information system
Publisher
Elsevier Masson
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201812175161Use this for linking
Review status
Peer reviewed
ISSN
0021-7824
DOI
https://doi.org/10.1016/j.matpur.2017.11.006
Language
English
Published in
Journal de Mathematiques Pures et Appliquees
Citation
- Le Donne, E., Pinamonti, A., & Speight, G. (2019). Universal differentiability sets and maximal directional derivatives in Carnot groups. Journal de Mathematiques Pures et Appliquees, 121, 83-112. https://doi.org/10.1016/j.matpur.2017.11.006
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Funder(s)
Research Council of Finland
European Commission
Funding program(s)
Akatemiatutkija, SA
ERC Starting Grant
Academy Research Fellow, AoF
ERC Starting Grant
Additional information about funding
E.L.D. is supported by the Academy of Finland grant 288501 and by the ERC Starting Grant 713998 GeoMeG. A.P. acknowledges the support of the Istituto Nazionale di Alta Matematica F. Severi. G.S. received support from the Charles Phelps Taft Research Center.
Copyright© 2017 Elsevier Masson SAS.