Maximal regularity for non-autonomous evolution equations
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HAAK, Bernhard Hermann | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, E.-M. | |
| dc.date.accessioned | 2024-04-04T03:18:45Z | |
| dc.date.available | 2024-04-04T03:18:45Z | |
| dc.date.created | 2014 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0025-5831 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194443 | |
| dc.description.abstractEn | We consider the maximal regularity problem for non-autonomous evolution equations of the form $u(t) + A(t) u(t) = f(t)$ with initial data $u(0) = u_0$ . Each operator $A(t)$ is associated with a sesquilinear form $a(t; *, *)$ on a Hilbert space $H$ . We assume that these forms all have the same domain and satisfy some regularity assumption with respect to t (e.g., piecewise $\alpha$-Hölder continuous for some $\alpha> 1/2$). We prove maximal Lp regularity for all initial values in the real-interpolation space $(H, D(A(0)))_{1/p,p}$ . The particular case where $p = 2$ improves previously known results and gives a positive answer to a question of J.L. Lions [11] on the set of allowed initial data $u_0$ . | |
| dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.rights.uri | http://hal.archives-ouvertes.fr/licences/copyright/ | |
| dc.subject.en | pseudo-differential operators | |
| dc.subject.en | Maximal regularity | |
| dc.subject.en | sesquilinear forms | |
| dc.subject.en | non-autonomous evolution equations | |
| dc.title.en | Maximal regularity for non-autonomous evolution equations | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1402.1136 | |
| bordeaux.journal | Mathematische Annalen | |
| bordeaux.page | 1-19 | |
| 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-00942422 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00942422v1 | |
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