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L1-Gradient Flow of Convex Functionals

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorChambolle, Antonin
HAL ID: 184536
ORCID: 0000-0002-9465-4659
hal.structure.identifierDipartimento di Matematica [Pisa]
dc.contributor.authorNovaga, Matteo
dc.date.accessioned2022-11-03T13:29:46Z
dc.date.available2022-11-03T13:29:46Z
dc.date.issued2022
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/23084
dc.language.isoenen
dc.subject.ddc515en
dc.titleL1-Gradient Flow of Convex Functionalsen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe are interested in the gradient flow of a general first order convex functional with respect to the L¹-topology. By means of an implicit minimization scheme, we show existence of a global limit solution, which satisfies an energy-dissipation estimate, and solves a non-linear and non-local gradient flow equation, under the assumption of strong convexity of the energy. Under a monotonicity assumption we can also prove uniqueness of the limit solution, even though this remains an open question in full generality. We also consider a geometric evolution corresponding to the L¹-gradient flow of the anisotropic perimeter. When the initial set is convex, we show that the limit solution is monotone for the inclusion, convex and unique until it reaches the Cheeger set of the initial datum. Eventually, we show with some examples that uniqueness cannot be expected in general in the geometric case.en
dc.publisher.cityParisen
dc.identifier.citationpages24en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSLen
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2022
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2022-11-03T13:27:38Z
hal.author.functionaut
hal.author.functionaut


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