Filters

20161

More filters

20221
Reset filters

Settings

End date: 2023 × Publisher: Dordrecht [u.a.] : Springer Science + Business Media B.V × Subject: Evolution equations × WGL Institute: WIAS ×

Search Results

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time
    (Dordrecht [u.a.] : Springer Science + Business Media B.V, 2016) Gallarati, Chiara; Veraar, Mark
    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.