Notions of Dirichlet problem for functions of least gradient in metric measure spaces
| dc.contributor.author | Korte, Riikka | |
| dc.contributor.author | Lahti, Panu | |
| dc.contributor.author | Li, Xining | |
| dc.contributor.author | Shanmugalingam, Nageswari | |
| dc.date.accessioned | 2019-11-12T13:11:53Z | |
| dc.date.available | 2019-11-12T13:11:53Z | |
| dc.date.issued | 2019 | |
| dc.identifier.citation | Korte, 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.other | CONVID_32170774 | |
| dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/66330 | |
| dc.description.abstract | We 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.mimetype | application/pdf | |
| dc.language | eng | |
| dc.language.iso | eng | |
| dc.publisher | European Mathematical Society Publishing House | |
| dc.relation.ispartofseries | Revista Matematica Iberoamericana | |
| dc.rights | In Copyright | |
| dc.subject.other | function of bounded variation | |
| dc.subject.other | inner trace | |
| dc.subject.other | perimeter | |
| dc.subject.other | least gradient | |
| dc.subject.other | p-harmonic | |
| dc.subject.other | Dirichlet problem | |
| dc.subject.other | metric measure space | |
| dc.subject.other | Poincaré inequality | |
| dc.subject.other | codimension 1 Hausdorff measure | |
| dc.title | Notions of Dirichlet problem for functions of least gradient in metric measure spaces | |
| dc.type | article | |
| dc.identifier.urn | URN:NBN:fi:jyu-201911124839 | |
| dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
| dc.contributor.laitos | Department of Mathematics and Statistics | en |
| dc.contributor.oppiaine | Matematiikka | fi |
| dc.contributor.oppiaine | Mathematics | 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 | 1603-1648 | |
| dc.relation.issn | 0213-2230 | |
| dc.relation.numberinseries | 6 | |
| dc.relation.volume | 35 | |
| dc.type.version | acceptedVersion | |
| dc.rights.copyright | © 2019 European Mathematical Society | |
| dc.rights.accesslevel | openAccess | fi |
| dc.format.content | fulltext | |
| dc.rights.url | http://rightsstatements.org/page/InC/1.0/?language=en | |
| dc.relation.doi | 10.4171/rmi/1095 | |
| jyx.fundinginformation | R. 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). | |
| dc.type.okm | A1 |
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