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Existence and uniqueness of ∞-harmonic functions under assumption of ∞-Poincaré inequality

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dc.contributor.authorDurand Cartagena, Estibalitz
dc.contributor.authorJaramillo, Jesús A.
dc.contributor.orcidhttps://orcid.org/0000-0002-0197-6449
dc.contributor.orcidhttps://orcid.org/0000-0002-2891-5064
dc.date.accessioned2024-12-03T12:48:40Z
dc.date.available2024-12-03T12:48:40Z
dc.date.issued2018-08-22
dc.descriptionThe registered version of this article, first published in Mathematische Annalen, is available online at the publisher's website: Springer Nature, https://doi.org/10.1007/s00208-018-1747-z
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en Mathematische Annalen, está disponible en línea en el sitio web del editor: Springer Nature, https://doi.org/10.1007/s00208-018-1747-z
dc.description.abstractGiven a complete metric measure space whose measure is doubling and supports an ∞- Poincar´e inequality, and a bounded domain Ω in such a space together with a Lipschitz function f : ∂Ω → R, we show the existence and uniqueness of an ∞-harmonic extension of f to Ω. To do so, we show that there is a metric that is bi-Lipschitz equivalent to the original metric, such that with respect to this new metric the metric space satisfies an ∞- weak Fubini property and that a function which is ∞-harmonic in the original metric must also be ∞-harmonic with respect to the new metric. We also show that if the metric on the metric space satisfies an ∞-weak Fubini property, then the notion of ∞-harmonic functions coincide with the notion of AMLEs proposed by Aronsson. The notion of ∞-harmonicity is in general distinct from the notion of strongly absolutely minimizing Lipschitz extensions found in [13, 25, 26], but coincides when the metric space supports a p-Poincar´e inequality for some finite p ≥ 1.en
dc.description.versionversión final
dc.identifier.citationDurand-Cartagena, E., Jaramillo, J.A. & Shanmugalingam, N. Existence and uniqueness of ∞-harmonic functions under assumption of ∞-Poincaré inequality. Math. Ann. 374, 881–906 (2019). https://doi.org/10.1007/s00208-018-1747-z
dc.identifier.doihttps://doi.org/10.1007/s00208-018-1747-z
dc.identifier.issn1432-1807
dc.identifier.urihttps://hdl.handle.net/20.500.14468/24672
dc.journal.issue374
dc.journal.titleMathematische Annalen
dc.language.isoen
dc.page.final906
dc.page.initial881
dc.publisherSpringer Nature
dc.relation.centerFacultades y escuelas::E.T.S. de Ingenieros Industriales
dc.relation.departmentMatemática Aplicada I
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywords∞-Poincar´e inequalityen
dc.subject.keywords∞-harmonicen
dc.subject.keywordsAMLEen
dc.subject.keywordsmetric measure spacesen
dc.titleExistence and uniqueness of ∞-harmonic functions under assumption of ∞-Poincaré inequalityen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
person.familyNameDurand Cartagena
person.givenNameEstibalitz
person.identifier.orcid0000-0001-6469-3633
relation.isAuthorOfPublicationd59ccac2-efd7-4059-9e2b-d7fc36689f85
relation.isAuthorOfPublication.latestForDiscoveryd59ccac2-efd7-4059-9e2b-d7fc36689f85
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