dc.contributor.author | Eriksson-Bique, Sylvester | |
dc.date.accessioned | 2023-02-15T10:07:34Z | |
dc.date.available | 2023-02-15T10:07:34Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Eriksson-Bique, S. (2023). Density of Lipschitz functions in energy. <i>Calculus of Variations and Partial Differential Equations</i>, <i>62</i>(2), Article 60. <a href="https://doi.org/10.1007/s00526-022-02395-1" target="_blank">https://doi.org/10.1007/s00526-022-02395-1</a> | |
dc.identifier.other | CONVID_176866437 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/85478 | |
dc.description.abstract | In this paper, we show that the density in energy of Lipschitz functions in a Sobolev space N1,p(X) holds for all p∈[1,∞) whenever the space X is complete and separable and the measure is Radon and positive and finite on balls. Emphatically, p=1 is allowed. We also give a few corollaries and pose questions for future work. The proof is direct and does not involve the usual flow techniques from prior work. It also yields a new approximation technique, which has not appeared in prior work. Notable with all of this work is that we do not use any form of Poincaré inequality or doubling assumption. The techniques are flexible and suggest a unification of a variety of approaches that have appeared in the literature on the topic. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | Springer Science and Business Media LLC | |
dc.relation.ispartofseries | Calculus of Variations and Partial Differential Equations | |
dc.rights | CC BY 4.0 | |
dc.title | Density of Lipschitz functions in energy | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202302151761 | |
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.relation.issn | 0944-2669 | |
dc.relation.numberinseries | 2 | |
dc.relation.volume | 62 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © 2022 the Authors | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 330048 | |
dc.subject.yso | funktionaalianalyysi | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p17780 | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.1007/s00526-022-02395-1 | |
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 author was supported by the Finnish Academy under Research Postdoctoral Grant No. 330048. | |
dc.type.okm | A1 | |