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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorACHACHE, Mahdi
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMAATI OUHABAZ, El
dc.date.accessioned2024-04-04T03:08:55Z
dc.date.available2024-04-04T03:08:55Z
dc.date.issued2019
dc.identifier.issn0022-0396
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193569
dc.description.abstractEnWe consider the problem of maximal regularity for non-autonomous Cauchy problems u ′ (t) + A(t) u(t) = f (t), t ∈ (0, τ ] u(0) = u 0. The time dependent operators A(t) are associated with (time dependent) sesquilinear forms on a Hilbert space H. We are interested in J.L. Lions's problem concerning maximal regularity of such equations. We give a positive answer to this problem under minimal regularity assumptions on the forms. Our main assumption is that the forms are piecewise H 1 2 with respect to the variable t. This regularity assumption is optimal and our results are the most general ones on this problem.
dc.language.isoen
dc.publisherElsevier
dc.subject.en47D06
dc.subject.ennon-autonomous evolution equations
dc.subject.enMaximal regularity
dc.subject.enSobolev regularity
dc.subject.enMathematics Subject Classification (2010): 35K90
dc.subject.en35K45
dc.title.enLions' maximal regularity problem with H 1/ 2 -regularity in time
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv1709.04216
bordeaux.journalJournal of Differential Equations
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01584987
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01584987v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Differential%20Equations&rft.date=2019&rft.eissn=0022-0396&rft.issn=0022-0396&rft.au=ACHACHE,%20Mahdi&MAATI%20OUHABAZ,%20El&rft.genre=article


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