Lions' maximal regularity problem with H 1/ 2 -regularity in time
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ACHACHE, Mahdi | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAATI OUHABAZ, El | |
| dc.date.accessioned | 2024-04-04T03:08:55Z | |
| dc.date.available | 2024-04-04T03:08:55Z | |
| dc.date.issued | 2019 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193569 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | 47D06 | |
| dc.subject.en | non-autonomous evolution equations | |
| dc.subject.en | Maximal regularity | |
| dc.subject.en | Sobolev regularity | |
| dc.subject.en | Mathematics Subject Classification (2010): 35K90 | |
| dc.subject.en | 35K45 | |
| dc.title.en | Lions' maximal regularity problem with H 1/ 2 -regularity in time | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1709.04216 | |
| bordeaux.journal | Journal of Differential Equations | |
| 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-01584987 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01584987v1 | |
| bordeaux.COinS | ctx_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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