Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time
dc.bibliographicCitation.date | 2017 | |
dc.bibliographicCitation.firstPage | 527 | eng |
dc.bibliographicCitation.issue | 3 | eng |
dc.bibliographicCitation.journalTitle | Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis | eng |
dc.bibliographicCitation.lastPage | 567 | eng |
dc.bibliographicCitation.volume | 46 | eng |
dc.contributor.author | Gallarati, Chiara | |
dc.contributor.author | Veraar, Mark | |
dc.date.accessioned | 2022-06-22T06:19:29Z | |
dc.date.available | 2022-06-22T06:19:29Z | |
dc.date.issued | 2016 | |
dc.description.abstract | In this paper we study maximal L p-regularity for evolution equations with time-dependent operators A. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the L p-boundedness of a class of vector-valued singular integrals which does not rely on Hörmander conditions in the time variable. This is then used to develop an abstract operator-theoretic approach to maximal regularity. The results are applied to the case of m-th order elliptic operators A with time and space-dependent coefficients. Here the highest order coefficients are assumed to be measurable in time and continuous in the space variables. This results in an L p(L q)-theory for such equations for p,q∈(1,∞). In the final section we extend a well-posedness result for quasilinear equations to the time-dependent setting. Here we give an example of a nonlinear parabolic PDE to which the result can be applied. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9113 | |
dc.identifier.uri | https://doi.org/10.34657/8151 | |
dc.language.iso | eng | eng |
dc.publisher | Dordrecht [u.a.] : Springer Science + Business Media B.V | eng |
dc.relation.doi | https://doi.org/10.1007/s11118-016-9593-7 | |
dc.relation.essn | 1572-929X | |
dc.rights.license | CC BY 4.0 Unported | eng |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | eng |
dc.subject.ddc | 510 | eng |
dc.subject.other | Ap-weights | eng |
dc.subject.other | Elliptic operators | eng |
dc.subject.other | Evolution equations | eng |
dc.subject.other | Extrapolation | eng |
dc.subject.other | Functional calculus | eng |
dc.subject.other | Maximal Lp-regularity | eng |
dc.subject.other | Quasi-linear PDE | eng |
dc.subject.other | R-boundedness | eng |
dc.subject.other | Singular integrals | eng |
dc.title | Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time | eng |
dc.type | Article | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Zeitschriftenartikel | eng |
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