Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds of gradient's blow-up for the Lam\'{e} system with
  partially infinite coefficients   In composite material, the stress may be arbitrarily large in the narrow
region between two close-to-touching hard inclusions. The stress is represented
by the gradient of a solution to the Lam\'{e} system of linear elasticity. The
aim of this paper is to establish lower bounds of the gradients of solutions of
the Lam\'{e} system with partially infinite coefficients as the distance
between the surfaces of discontinuity of the coefficients of the system tends
to zero. Combining it with the pointwise upper bounds obtained in our previous
work, the optimality of the blow-up rate of gradients is proved for inclusions
with arbitrary shape in dimensions two and three. The key to show this is that
we find a blow-up factor, a linear functional of the boundary data, to
determine whether the blow-up will occur or not.

36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
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
15
The categories of this paper are: nucl-ex