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MAXIMAL REGULARITY FOR NON-AUTONOMOUS EVOLUTION EQUATIONS GOVERNED BY FORMS HAVING LESS REGULARITY

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorOUHABAZ, El Maati
dc.date.accessioned2024-04-04T03:20:15Z
dc.date.available2024-04-04T03:20:15Z
dc.date.issued2015
dc.identifier.issn0003-889X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194575
dc.description.abstractEnWe consider the maximal regularity problem for non-autonomous evolution equa-tions u (t) + A(t) u(t) = f (t), t ∈ (0, τ ] u(0) = u 0 . (0.1) Each operator A(t) is associated with a sesquilinear form a(t) on a Hilbert space H. We as-sume that these forms all have the same domain V . It is proved in [11] that if the forms have some regularity with respect to t (e.g., piecewise α-Hölder continuous for some α > 1 /2) then the above problem has maximal Lp–regularity for all u 0 in the real-interpolation space (H, D(A(0))) 1−1/p,p . In this paper we prove that the regularity required there can be im-proved for a class of sesquilinear forms. The forms considered here are such that the difference a(t; ·, ·) − a(s; ·, ·) is continuous on a larger space than the common domain V . We give three examples which illustrate our results.
dc.description.sponsorshipAux frontières de l'analyse Harmonique - ANR-12-BS01-0013
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enMAXIMAL REGULARITY FOR NON-AUTONOMOUS EVOLUTION EQUATIONS GOVERNED BY FORMS HAVING LESS REGULARITY
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalArchiv der Mathematik
bordeaux.page79-91
bordeaux.volume105
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01079427
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01079427v1
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