Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition and pointwise estimates of periodic Green functions of
  some elliptic equations with periodic oscillatory coefficients   This article is about the $\mathbb{Z}^d$-periodic Green function $G_n(x,y)$
of the multiscale elliptic operator $Lu=-{\rm div}\left( A(n\cdot) \cdot \nabla
u \right)$, where $A(x)$ is a $\mathbb{Z}^d$-periodic, coercive, and H\"older
continuous matrix, and $n$ is a large integer. We prove here pointwise
estimates on $G_n(x,y)$, $\nabla_x G_n(x,y)$, $\nabla_y G_n(x,y)$ and $\nabla_x
\nabla_y G_n(x,y)$ in dimensions $d \geq 2$. Moreover, we derive an explicit
decomposition of this Green function, which is of independent interest. These
results also apply for systems.

30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org