Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularities of the stress concentration in the presence of
  $C^{1,\alpha}$-inclusions with core-shell geometry   In high-contrast composites, if an inclusion is in close proximity to the
matrix boundary, then the stress, which is represented by the gradient of a
solution to the Lam\'{e} systems of linear elasticity, may exhibits the
singularities with respect to the distance $\varepsilon$ between them. In this
paper, we establish the asymptotic formulas of the stress concentration for
core-shell geometry with $C^{1,\alpha}$ boundaries in all dimensions by
precisely capturing all the blow-up factor matrices, as the distance
$\varepsilon$ between interfacial boundaries of a core and a surrounding shell
goes to zero. Further, a direct application of these blow-up factor matrices
gives the optimal gradient estimates.

29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph