Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An integral-representation result for continuum limits of discrete
  energies with multi-body interactions   We prove a compactness and integral-representation theorem for sequences of
families of lattice energies describing atomistic interactions defined on
lattices with vanishing lattice spacing. The densities of these energies may
depend on interactions between all points of the corresponding lattice
contained in a reference set. We give conditions that ensure that the limit is
an integral defined on a Sobolev space. A homogenization theorem is also
proved. The result is applied to multibody interactions corresponding to
discrete Jacobian determinants and to linearizations of Lennard-Jones energies
with mixtures of convex and concave quadratic pair-potentials.

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The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex