Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A finer singular limit of a single-well Modica--Mortola functional and
  its applications to the Kobayashi--Warren--Carter energy   An explicit representation of the Gamma limit of a single-well
Modica--Mortola functional is given for one-dimensional space under the graph
convergence which is finer than conventional $L^1$-convergence or convergence
in measure. As an application, an explicit representation of a singular limit
of the Kobayashi-Warren-Carter energy, which is popular in materials science,
is given. Some compactness under the graph convergence is also established.
Such formulas, as well as compactness, is useful to characterize the limit of
minimizers the Kobayashi-Warren-Carter energy. To characterize the Gamma limit
under the graph convergence, a new idea which is especially useful for
one-dimensional problem is introduced. It is a change of parameter of the
variable by arc-length parameter of its graph, which is called unfolding by the
arc-length parameter in this paper.

35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph