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Medientyp:
Sonstige Veröffentlichung;
E-Artikel
Titel:
Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time
Beteiligte:
Gallarati, Chiara
[VerfasserIn];
Veraar, Mark
[VerfasserIn]
Erschienen:
Dordrecht [u.a.] : Springer Science + Business Media B.V, 2016
Erschienen in:Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis 46 (2017), Nr. 3
Anmerkungen:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Beschreibung:
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.