Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Progress on the Strong Eshelby's Conjecture and Extremal Structures for
  the Elastic Moment Tensor   We make progress towards proving the strong Eshelby's conjecture in three
dimensions. We prove that if for a single nonzero uniform loading the strain
inside inclusion is constant and further the eigenvalues of this strain are
either all the same or all distinct, then the inclusion must be of ellipsoidal
shape. As a consequence, we show that for two linearly independent loadings the
strains inside the inclusions are uniform, then the inclusion must be of
ellipsoidal shape. We then use this result to address a problem of determining
the shape of an inclusion when the elastic moment tensor (elastic
polarizability tensor) is extremal. We show that the shape of inclusions, for
which the lower Hashin-Shtrikman bound either on the bulk part or on the shear
part of the elastic moment tensor is attained, is an ellipse in two dimensions
and an ellipsoid in three dimensions.

15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin