Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradient estimates for electric fields with multi-scale inclusions in
  the quasi-static regime   In this paper, we are concerned with the gradient estimate of the electric
field due to two nearly touching dielectric inclusions, which is a central
topic in the theory of composite materials. We derive accurate quantitative
characterisations of the gradient fields in the transverse electromagnetic case
within the quasi-static regime, which clearly indicate the optimal blowup rate
or non-blowup of the gradient fields in different scenarios. There are mainly
two novelties of our study. First, the sizes of the two material inclusions may
be of different scales. Second, we consider our study in the quasi-static
regime, whereas most of the existing studies are concerned with the static
case.

20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph