On the integration of L0-Banach L0-modules and its applications to vector calculus on RCD spaces
| dc.contributor.author | Caputo, Emanuele | |
| dc.contributor.author | Lučić, Milica | |
| dc.contributor.author | Pasqualetto, Enrico | |
| dc.contributor.author | Vojnović, Ivana | |
| dc.date.accessioned | 2024-05-15T08:29:24Z | |
| dc.date.available | 2024-05-15T08:29:24Z | |
| dc.date.issued | 2024 | |
| dc.identifier.citation | Caputo, E., Lučić, M., Pasqualetto, E., & Vojnović, I. (2024). On the integration of L0-Banach L0-modules and its applications to vector calculus on RCD spaces. <i>Revista Matemática Complutense</i>, <i>Early online</i>. <a href="https://doi.org/10.1007/s13163-024-00491-8" target="_blank">https://doi.org/10.1007/s13163-024-00491-8</a> | |
| dc.identifier.other | CONVID_213668005 | |
| dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/94837 | |
| dc.description.abstract | A finite-dimensional RCD space can be foliated into sufficiently regular leaves, where a differential calculus can be performed. Two important examples are given by the measure-theoretic boundary of the superlevel set of a function of bounded variation and the needle decomposition associated to a Lipschitz function. The aim of this paper is to connect the vector calculus on the lower dimensional leaves with the one on the base space. In order to achieve this goal, we develop a general theory of integration of L0-Banach L0-modules of independent interest. Roughly speaking, we study how to ‘patch together’ vector fields defined on the leaves that are measurable with respect to the foliation parameter. | fi |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | eng | |
| dc.publisher | Springer | |
| dc.relation.ispartofseries | Revista Matemática Complutense | |
| dc.rights | CC BY 4.0 | |
| dc.subject.other | L0-Banach L0-module | |
| dc.subject.other | integration | |
| dc.subject.other | RCD space | |
| dc.subject.other | BV function | |
| dc.subject.other | needle decomposition | |
| dc.title | On the integration of L0-Banach L0-modules and its applications to vector calculus on RCD spaces | |
| dc.type | article | |
| dc.identifier.urn | URN:NBN:fi:jyu-202405153607 | |
| 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 | 1139-1138 | |
| dc.relation.volume | Early online | |
| dc.type.version | publishedVersion | |
| dc.rights.copyright | © The Author(s) 2024 | |
| dc.rights.accesslevel | openAccess | fi |
| dc.relation.grantnumber | 314789 | |
| dc.format.content | fulltext | |
| dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
| dc.relation.doi | 10.1007/s13163-024-00491-8 | |
| dc.relation.funder | Research Council of Finland | en |
| dc.relation.funder | Suomen Akatemia | fi |
| jyx.fundingprogram | Academy Project, AoF | en |
| jyx.fundingprogram | Akatemiahanke, SA | fi |
| jyx.fundinginformation | E.C. acknowledges the support from the Academy of Finland, grants no. 314789 and 321896. M. L. and I. V. gratefully acknowledge the financial support of the Ministry of Science, Technological Development and Innovation of the Republic of Serbia (Grants No. 451-03-66/2024-03/ 200125 & 451-03-65/2024-03/200125). | |
| dc.type.okm | A1 |
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