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dc.contributor.authorLe Donne, Enrico
dc.contributor.authorPinamonti, Andrea
dc.contributor.authorSpeight, Gareth
dc.date.accessioned2018-12-18T10:19:07Z
dc.date.available2021-02-01T22:35:09Z
dc.date.issued2019
dc.identifier.citationLe 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.otherCONVID_27355410
dc.identifier.otherTUTKAID_75712
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/60646
dc.description.abstractWe 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.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier Masson
dc.relation.ispartofseriesJournal de Mathematiques Pures et Appliquees
dc.rightsCC BY-NC-ND 4.0
dc.subject.otherCarnot group
dc.subject.otherLipschitz map
dc.subject.otherPansu differentiable
dc.subject.otherdirectional derivative
dc.subject.otheruniversal differentiability set
dc.titleUniversal differentiability sets and maximal directional derivatives in Carnot groups
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201812175161
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2018-12-17T10:15:32Z
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange83-112
dc.relation.issn0021-7824
dc.relation.numberinseries0
dc.relation.volume121
dc.type.versionacceptedVersion
dc.rights.copyright© 2017 Elsevier Masson SAS.
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber288501
dc.relation.grantnumber713998
dc.relation.grantnumber713998
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/713998/EU//GeoMeG
dc.subject.ysodifferentiaaligeometria
dc.subject.ysofunktionaalianalyysi
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p16682
jyx.subject.urihttp://www.yso.fi/onto/yso/p17780
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1016/j.matpur.2017.11.006
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
dc.relation.funderResearch Council of Finlanden
dc.relation.funderEuropean Commissionen
jyx.fundingprogramAkatemiatutkija, SAfi
jyx.fundingprogramERC Starting Grantfi
jyx.fundingprogramAcademy Research Fellow, AoFen
jyx.fundingprogramERC Starting Granten
jyx.fundinginformationE.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.okmA1


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