Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonconvex minimization related to quadratic double-well energy -
  approximation by convex problems   A double-well energy expressed as a minimum of two quadratic functions,
called phase energies, is studied with taking into account the minimization of
the corresponding integral functional. Such integral, as being not sequentially
weakly lower semicontinuous, does not admit classical minimizers. To derive the
relaxation formula for the infimum, the minimizing sequence consisting of
solutions of convex problems appropriately approximating the original nonconvex
one is constructed. The weak limit of this sequence together with the weak
limit of the sequence of solutions of the corresponding dual problems and the
weak limits of the characteristic functions related to the phase energies are
involved in the relaxation formula.

27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio