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A note on the rearrangement of functions in time and on the parabolic Talenti inequality

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorMazari, Idriss
HAL ID: 751069
dc.date.accessioned2022-04-21T11:35:59Z
dc.date.available2022-04-21T11:35:59Z
dc.date.issued2022
dc.identifier.issn0430-3202
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22894
dc.language.isoenen
dc.subjectOptimisationen
dc.subjectOptimal control of PDEsen
dc.subjectRearrangement of functionsen
dc.subjectTalenti inequalityen
dc.subject.ddc515en
dc.titleA note on the rearrangement of functions in time and on the parabolic Talenti inequalityen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenTalenti inequalities are a central feature in the qualitative analysis of PDE constrained optimal control as well as in calculus of variations. The classical parabolic Talenti inequality states that if we consider the parabolic equation ∂u ∂t − ∆u = f = f (t, x) then, replacing, for any time t, f (t, •) with its Schwarz rearrangement f # (t, •) increases the concentration of the solution in the following sense: letting v be the solution of ∂v ∂t − ∆v = f # in the ball, then the solution u is less concentrated than v. This property can be rephrased in terms of the existence of a maximal element for a certain order relationship. It is natural to try and rearrange the source term not only in space but also in time, and thus to investigate the existence of such a maximal element when we rearrange the function with respect to the two variables. In the present paper we prove that this is not possible.en
dc.relation.isversionofjnlnameAnnali Dell'Universita' Di Ferrara
dc.relation.isversionofjnldate2022-03
dc.relation.isversionofdoi10.1007/s11565-022-00392-yen
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2022-04-21T11:29:59Z
hal.author.functionaut


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