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dc.contributor.authorJulin, Vesa
dc.date.accessioned2024-04-25T07:28:41Z
dc.date.available2024-04-25T07:28:41Z
dc.date.issued2024
dc.identifier.citationJulin, V. (2024). Flat flow solution to the mean curvature flow with volume constraint. <i>Advances in Calculus of Variations</i>, <i>Early online</i>. <a href="https://doi.org/10.1515/acv-2023-0047" target="_blank">https://doi.org/10.1515/acv-2023-0047</a>
dc.identifier.otherCONVID_213311943
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/94472
dc.description.abstractIn this paper I will revisit the construction of a global weak solution to the volume preserving mean curvature flow via discrete minimizing movement scheme by Mugnai, Seis and Spadaro [L. Mugnai, C. Seis and E. Spadaro, Global solutions to the volume-preserving mean-curvature flow, Calc. Var. Partial Differential Equations 55 2016, 1, Article ID 18]. This method is based on the gradient flow approach due to Almgren, Taylor and Wang [F. Almgren, J. E. Taylor and L. Wang, Curvature-driven flows: a variational approach, SIAM J. Control Optim. 31 1993, 2, 387–438] and Luckhaus and Sturzenhecker [S. Luckhaus and T. Sturzenhecker, Implicit time discretization for the mean curvature flow equation, Calc. Var. Partial Differential Equations 3 1995, 2, 253–271] and my aim is to replace the volume penalization with the volume constraint directly in the discrete scheme, which from practical point of view is perhaps more natural. A technical novelty is the proof of the density estimate which is based on second variation argumenten
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherWalter de Gruyter GmbH
dc.relation.ispartofseriesAdvances in Calculus of Variations
dc.rightsCC BY 4.0
dc.subject.otherMean-curvature flow
dc.subject.othervolume constraint
dc.subject.othergradient flow
dc.subject.othertime discretization
dc.titleFlat flow solution to the mean curvature flow with volume constraint
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202404253099
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.relation.issn1864-8258
dc.relation.volumeEarly online
dc.type.versionpublishedVersion
dc.rights.copyright© 2024 the author(s), published by De Gruyter
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber314227
dc.relation.grantnumber347550
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.subject.ysodifferentiaaligeometria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
jyx.subject.urihttp://www.yso.fi/onto/yso/p16682
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1515/acv-2023-0047
dc.relation.funderResearch Council of Finlanden
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramResearch costs of Academy Research Fellow, AoFen
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAkatemiatutkijan tutkimuskulut, SAfi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundinginformationThe author is supported by the Academy of Finland, grants no. 314227 and no. 347550.
dc.type.okmA1


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