dc.contributor.author | Eriksson-Bique, Sylvester | |
dc.contributor.author | Poggi-Corradini, Pietro | |
dc.date.accessioned | 2024-08-15T10:24:01Z | |
dc.date.available | 2024-08-15T10:24:01Z | |
dc.date.issued | 2024 | |
dc.identifier.citation | Eriksson-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.other | CONVID_233351160 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/96612 | |
dc.description.abstract | We 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.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | American Mathematical Society (AMS) | |
dc.relation.ispartofseries | Transactions of the American Mathematical Society : Series B | |
dc.rights | CC BY 3.0 | |
dc.title | Density of continuous functions in Sobolev spaces with applications to capacity | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202408155496 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 901-944 | |
dc.relation.issn | 2330-0000 | |
dc.relation.volume | 11 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © 2024 the Authors | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 356861 | |
dc.subject.yso | potentiaaliteoria | |
dc.subject.yso | metriset avaruudet | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p18911 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p27753 | |
dc.rights.url | https://creativecommons.org/licenses/by/3.0/ | |
dc.relation.doi | 10.1090/btran/188 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | Postdoctoral Researcher, AoF | en |
jyx.fundingprogram | Tutkijatohtori, SA | fi |
jyx.fundinginformation | The 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.okm | A1 | |