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dc.contributor.authorKorte, Riikka
dc.contributor.authorLahti, Panu
dc.contributor.authorLi, Xining
dc.contributor.authorShanmugalingam, Nageswari
dc.date.accessioned2019-11-12T13:11:53Z
dc.date.available2019-11-12T13:11:53Z
dc.date.issued2019
dc.identifier.citationKorte, R., Lahti, P., Li, X., & Shanmugalingam, N. (2019). Notions of Dirichlet problem for functions of least gradient in metric measure spaces. <i>Revista Matematica Iberoamericana</i>, <i>35</i>(6), 1603-1648. <a href="https://doi.org/10.4171/rmi/1095" target="_blank">https://doi.org/10.4171/rmi/1095</a>
dc.identifier.otherCONVID_32170774
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/66330
dc.description.abstractWe study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazón-Rossi–De León, solutions by considering the Dirichlet problem for p-harmonic functions, p>1, and letting p→1. Tools developed and used in this paper include the inner perimeter measure of a domain.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherEuropean Mathematical Society Publishing House
dc.relation.ispartofseriesRevista Matematica Iberoamericana
dc.rightsIn Copyright
dc.subject.otherfunction of bounded variation
dc.subject.otherinner trace
dc.subject.otherperimeter
dc.subject.otherleast gradient
dc.subject.otherp-harmonic
dc.subject.otherDirichlet problem
dc.subject.othermetric measure space
dc.subject.otherPoincaré inequality
dc.subject.othercodimension 1 Hausdorff measure
dc.titleNotions of Dirichlet problem for functions of least gradient in metric measure spaces
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201911124839
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.pagerange1603-1648
dc.relation.issn0213-2230
dc.relation.numberinseries6
dc.relation.volume35
dc.type.versionacceptedVersion
dc.rights.copyright© 2019 European Mathematical Society
dc.rights.accesslevelopenAccessfi
dc.format.contentfulltext
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.4171/rmi/1095
jyx.fundinginformationR. Korte was supported by Academy of Finland grant number 308063, P. Lahti was supported by a grant from the Finnish Cultural Foundation, and X. Li was supported by NNSF of China (No. 11701582). The research of N. Shanmugalingam is partially supported by the grant # DMS–1500440 of NSF (USA).


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