MAXIMAL REGULARITY FOR NON-AUTONOMOUS EVOLUTION EQUATIONS GOVERNED BY FORMS HAVING LESS REGULARITY
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T03:20:15Z | |
| dc.date.available | 2024-04-04T03:20:15Z | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0003-889X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194575 | |
| dc.description.abstractEn | We 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.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.title.en | MAXIMAL REGULARITY FOR NON-AUTONOMOUS EVOLUTION EQUATIONS GOVERNED BY FORMS HAVING LESS REGULARITY | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Archiv der Mathematik | |
| bordeaux.page | 79-91 | |
| bordeaux.volume | 105 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01079427 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01079427v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Archiv%20der%20Mathematik&rft.date=2015&rft.volume=105&rft.spage=79-91&rft.epage=79-91&rft.eissn=0003-889X&rft.issn=0003-889X&rft.au=OUHABAZ,%20El%20Maati&rft.genre=article |
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