Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of phase-field approximations to the Gibbs-Thomson law   We prove the convergence of phase-field approximations of the Gibbs-Thomson
law. This establishes a relation between the first variation of the
Van-der-Waals-Cahn-Hilliard energy and the first variation of the area
functional. We allow for folding of diffuse interfaces in the limit and the
occurrence of higher-multiplicities of the limit energy measures. We show that
the multiplicity does not affect the Gibbs-Thomson law and that the mean
curvature vanishes where diffuse interfaces have collided.
  We apply our results to prove the convergence of stationary points of the
Cahn-Hilliard equation to constant mean curvature surfaces and the convergence
of stationary points of an energy functional that was proposed by Ohta-Kawasaki
as a model for micro-phase separation in block-copolymers.

27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg