Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time
By C. Gallarati, Mark Veraar. 2014
59 citations recorded by the source corpus.
In this paper we study maximal Lp-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 Lp-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 Lp(Lq)-theory for such equations for p,q∈(1,∞)$p,q\in (1, \infty )$. 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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2e041df25d55a3130a6352fd7b9ca2be3a430ae5
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights (2016, background): “t !1/q , 1 <p<q<∞. When the coefficients are VMO in xand independent with respect to t, mixed-norm estimates for parabolic systems in non-divergence form were established in [29]. Recently, in [26] Gallarati and Veraar proved Lp,q-estimates for any p,q∈ (1,∞) when the coefficients are uniformly”