Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal estimates for the conductivity problem by Green's function
  method   We study a class of second-order elliptic equations of divergence form, with
discontinuous coefficients and data, which models the conductivity problem in
composite materials. We establish optimal gradient estimates by showing the
explicit dependence of the elliptic coefficients and the distance between
interfacial boundaries of inclusions. The novelty of these estimates is that
they unify the known results in the literature and answer open problem (b)
proposed by Li-Vogelius (2000) for the isotropic conductivity problem. We also
obtain more interesting higher-order derivative estimates, which answers open
problem (c) of Li-Vogelius (2000). It is worth pointing out that the equations
under consideration in this paper are nonhomogeneous.

16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg