Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal regularity for non-autonomous equations with measurable
  dependence on time   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 H\"ormander 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 $p,q\in (1,
\infty)$.
  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.

13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn