Universal differentiability sets and maximal directional derivatives in Carnot groups

Le Donne, Enrico; Pinamonti, Andrea; Speight, Gareth

doi:10.1016/j.matpur.2017.11.006

dc.contributor.author	Le Donne, Enrico
dc.contributor.author	Pinamonti, Andrea
dc.contributor.author	Speight, Gareth
dc.date.accessioned	2018-12-18T10:19:07Z
dc.date.available	2021-02-01T22:35:09Z
dc.date.issued	2019
dc.identifier.citation	Le Donne, E., Pinamonti, A., & Speight, G. (2019). Universal differentiability sets and maximal directional derivatives in Carnot groups. <i>Journal de Mathematiques Pures et Appliquees</i>, <i>121</i>, 83-112. <a href="https://doi.org/10.1016/j.matpur.2017.11.006" target="_blank">https://doi.org/10.1016/j.matpur.2017.11.006</a>
dc.identifier.other	CONVID_27355410
dc.identifier.other	TUTKAID_75712
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/60646
dc.description.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.	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Elsevier Masson
dc.relation.ispartofseries	Journal de Mathematiques Pures et Appliquees
dc.rights	CC BY-NC-ND 4.0
dc.subject.other	Carnot group
dc.subject.other	Lipschitz map
dc.subject.other	Pansu differentiable
dc.subject.other	directional derivative
dc.subject.other	universal differentiability set
dc.title	Universal differentiability sets and maximal directional derivatives in Carnot groups
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-201812175161
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.contributor.oppiaine	Matematiikka	fi
dc.contributor.oppiaine	Mathematics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.date.updated	2018-12-17T10:15:32Z
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	83-112
dc.relation.issn	0021-7824
dc.relation.numberinseries	0
dc.relation.volume	121
dc.type.version	acceptedVersion
dc.rights.copyright	© 2017 Elsevier Masson SAS.
dc.rights.accesslevel	openAccess	fi
dc.relation.grantnumber	288501
dc.relation.grantnumber	713998
dc.relation.grantnumber	713998
dc.relation.projectid	info:eu-repo/grantAgreement/EC/H2020/713998/EU//GeoMeG
dc.subject.yso	differentiaaligeometria
dc.subject.yso	funktionaalianalyysi
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p16682
jyx.subject.uri	http://www.yso.fi/onto/yso/p17780
dc.rights.url	https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi	10.1016/j.matpur.2017.11.006
dc.relation.funder	Suomen Akatemia	fi
dc.relation.funder	Euroopan komissio	fi
dc.relation.funder	Research Council of Finland	en
dc.relation.funder	European Commission	en
jyx.fundingprogram	Akatemiatutkija, SA	fi
jyx.fundingprogram	ERC Starting Grant	fi
jyx.fundingprogram	Academy Research Fellow, AoF	en
jyx.fundingprogram	ERC Starting Grant	en
jyx.fundinginformation	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.
dc.type.okm	A1