Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization of Elliptic Systems with Neumann Boundary Conditions   The main purpose of this work is to study uniform regularity estimates for a
family of elliptic operators $\{\mathcal{L}_\varepsilon, \varepsilon>0\}$,
arising in the theory of homogenization, with rapidly oscillating periodic
coefficients. We establish sharp $W^{1,p}$ estimates, Lipschitz estimates, and
nontangential maximal function estimates, which are uniform in the parameter
$\varepsilon$, on solutions with Neumann boundary conditions in $C^{1,\alpha}$
domains.

34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph