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An Extension Theorem for convex functions of class C1,1 on Hilbert spaces

dc.contributor.authorAzagra Rueda, Daniel
dc.contributor.authorMudarra, C.
dc.date.accessioned2023-06-17T21:51:07Z
dc.date.available2023-06-17T21:51:07Z
dc.date.issued2017
dc.description.abstractLet H be a Hilbert space, E⊂H be an arbitrary subset and f:E→R, G:E→H be two functions. We give a necessary and sufficient condition on the pair (f,G) for the existence of a convex function F∈C1,1(H) such that F=f and ∇F=G on E. We also show that, if this condition is met, F can be taken so that Lip(∇F)=Lip(G). We give a geometrical application of this result, concerning interpolation of sets by boundaries of C1,1 convex bodies in H. Finally, we give a counterexample to a related question concerning smooth convex extensions of smooth convex functions with derivatives which are not uniformly continuous.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Economía y Competitividad (MINECO)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/41483
dc.identifier.doi10.1016/j.jmaa.2016.09.015
dc.identifier.issn0022-247X
dc.identifier.officialurlhttp://www.sciencedirect.com/science/article/pii/S0022247X16305182
dc.identifier.relatedurlhttp://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/17649
dc.issue.number2
dc.journal.titleJournal of Mathematical Analysis and Applications
dc.language.isoeng
dc.page.final1182
dc.page.initial1167
dc.publisherElsevier
dc.relation.projectIDMTM2012-34341
dc.rights.accessRightsrestricted access
dc.subject.cdu517
dc.subject.keywordC1
dc.subject.keyword1 function
dc.subject.keywordConvex function
dc.subject.keywordWhitney extension theorem
dc.subject.ucmAnálisis matemático
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleAn Extension Theorem for convex functions of class C1,1 on Hilbert spaces
dc.typejournal article
dc.volume.number446
dspace.entity.typePublication
relation.isAuthorOfPublication6696556b-dc2e-4272-8f5f-fa6a7a2f5344
relation.isAuthorOfPublication.latestForDiscovery6696556b-dc2e-4272-8f5f-fa6a7a2f5344

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