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dc.contributor.authorBjörn, Anders
dc.contributor.authorBjörn, Jana
dc.contributor.authorLehrbäck, Juha
dc.date.accessioned2020-06-11T10:17:18Z
dc.date.available2020-06-11T10:17:18Z
dc.date.issued2020
dc.identifier.citationBjörn, A., Björn, J., & Lehrbäck, J. (2020). Existence and almost uniqueness for p-harmonic Green functions on bounded domains in metric spaces. <i>Journal of Differential Equations</i>, <i>269</i>(9), 6602-6640. <a href="https://doi.org/10.1016/j.jde.2020.04.044" target="_blank">https://doi.org/10.1016/j.jde.2020.04.044</a>
dc.identifier.otherCONVID_35919064
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/69879
dc.description.abstractWe study (p-harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only if the complement of the domain has positive capacity, and that they satisfy very precise capacitary identities for superlevel sets. Suitably normalized singular functions are called Green functions. Uniqueness of Green functions is largely an open problem beyond unweighted Rn, but we show that all Green functions (in a given domain and with the same singularity) are comparable. As a consequence, for p-harmonic functions with a given pole we obtain a similar comparison result near the pole. Various characterizations of singular functions are also given. Our results hold in complete metric spaces with a doubling measure supporting a p-Poincaré inequality, or under similar local assumptions.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofseriesJournal of Differential Equations
dc.rightsCC BY 4.0
dc.subject.othercapacitary potential
dc.subject.otherdoubling measure
dc.subject.othermetric space
dc.subject.otherp-harmonic
dc.subject.othergreen function
dc.subject.otherPoincaré inequality
dc.subject.othersingular function
dc.titleExistence and almost uniqueness for p-harmonic Green functions on bounded domains in metric spaces
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202006114124
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.description.reviewstatuspeerReviewed
dc.format.pagerange6602-6640
dc.relation.issn0022-0396
dc.relation.numberinseries9
dc.relation.volume269
dc.type.versionpublishedVersion
dc.rights.copyright© 2020 The Authors. Published by Elsevier Inc
dc.rights.accesslevelopenAccessfi
dc.subject.ysopotentiaaliteoria
dc.subject.ysometriset avaruudet
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p18911
jyx.subject.urihttp://www.yso.fi/onto/yso/p27753
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1016/j.jde.2020.04.044
jyx.fundinginformationA.B. and J.B. were supported by the Swedish Research Council, grants 2016-03424 and 621-2014-3974, respectively. J.L. was supported by the Academy of Finland, grant 252108.


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