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A well-posedness result for hyperbolic operators with Zygmund coefficients

hal.structure.identifierDipartimento di Matematica
dc.contributor.authorCOLOMBINI, Ferruccio
hal.structure.identifierUniversità degli studi di Trieste = University of Trieste
dc.contributor.authorDEL SANTO, Daniele
hal.structure.identifierLaboratoire d'Analyse et de Mathématiques Appliquées [LAMA]
dc.contributor.authorFANELLI, Francesco
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMETIVIER, Guy
dc.date.accessioned2024-04-04T02:24:35Z
dc.date.available2024-04-04T02:24:35Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189827
dc.description.abstractEnIn this paper we prove an energy estimate with no loss of derivatives for a strictly hyperbolic operator with Zygmund continuous second order coe fficients both in time and in space. In particular, this estimate implies the well-posedness for the related Cauchy problem. On the one hand, this result is quite surprising, because it allows to consider coe cients which are not Lipschitz continuous in time. On the other hand, it holds true only in the very special case of initial data in H^(1/2) - H^(-1/2). Paradi erential calculus with parameters is the main ingredient to the proof.
dc.language.isoen
dc.title.enA well-posedness result for hyperbolic operators with Zygmund coefficients
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.description.sponsorshipEuropeNew analytical and numerical methods in wave propagation
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00733564
hal.version1
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00733564v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=COLOMBINI,%20Ferruccio&DEL%20SANTO,%20Daniele&FANELLI,%20Francesco&METIVIER,%20Guy&rft.genre=preprint


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