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dc.contributor.authorEriksson-Bique, Sylvester
dc.contributor.authorPoggi-Corradini, Pietro
dc.date.accessioned2024-08-15T10:24:01Z
dc.date.available2024-08-15T10:24:01Z
dc.date.issued2024
dc.identifier.citationEriksson-Bique, S., & Poggi-Corradini, P. (2024). Density of continuous functions in Sobolev spaces with applications to capacity. <i>Transactions of the American Mathematical Society : Series B</i>, <i>11</i>, 901-944. <a href="https://doi.org/10.1090/btran/188" target="_blank">https://doi.org/10.1090/btran/188</a>
dc.identifier.otherCONVID_233351160
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/96612
dc.description.abstractWe show that capacity can be computed with locally Lipschitz functions in locally complete and separable metric spaces. Further, we show that if (X, d, μ) is a locally complete and separable metric measure space, then continuous functions are dense in the Newtonian space N1,p (X). Here the measure μ is Borel and is finite and positive on all metric balls. In particular, we don’t assume properness of X, doubling of μ or any Poincaré inequali-ties. These resolve, partially or fully, questions posed by a number of authors, including J. Heinonen, A. Björn and J. Björn. In contrast to much of the past work, our results apply to locally complete spaces X and dispenses with the frequently used regularity assumptions: doubling, properness, Poincaré inequality, Loewner property or quasiconvexity.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Mathematical Society (AMS)
dc.relation.ispartofseriesTransactions of the American Mathematical Society : Series B
dc.rightsCC BY 3.0
dc.titleDensity of continuous functions in Sobolev spaces with applications to capacity
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202408155496
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange901-944
dc.relation.issn2330-0000
dc.relation.volume11
dc.type.versionpublishedVersion
dc.rights.copyright© 2024 the Authors
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber356861
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/3.0/
dc.relation.doi10.1090/btran/188
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramPostdoctoral Researcher, AoFen
jyx.fundingprogramTutkijatohtori, SAfi
jyx.fundinginformationThe first author was partially supported by Finnish Academy Grants n. 345005 and n. 356861. The second author was partially supported by NSF DMS n. 2154032.
dc.type.okmA1


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