Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The higher order regularity Dirichlet problem for elliptic systems in
  the upper-half space   We identify a large class of constant (complex) coefficient, second order
elliptic systems for which the Dirichlet problem in the upper-half space with
data in $L^p$-based Sobolev spaces, $1<p<\infty$, of arbitrary smoothness
$\ell$, is well-posed in the class of functions whose nontangential maximal
operator of their derivatives up to, and including, order $\ell$ is
$L^p$-integrable. This class includes all scalar, complex coefficient elliptic
operators of second order, as well as the Lam\'e system of elasticity, among
others.

33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int