# $\Gamma$-type estimates for the one-dimensional Allen-Cahn's action

created by novaga on 23 Jul 2013
modified on 07 Jan 2016

[BibTeX]

Published Paper

Inserted: 23 jul 2013
Last Updated: 7 jan 2016

Journal: Asymptotic Analysis
Volume: 94
Number: 1-2
Pages: 161-185
Year: 2015

Abstract:

In this paper we prove an asymptotic estimate, up to the second order included, on the behaviour of the one-dimensional Allen-Cahn's action functionals, around a periodic function with bounded variation and taking values in $\pm 1$. The leading order term of this estimate justifi es and con firms, from a variational point of view, the results of Fusco-Hale and Carr-Pego on the exponentially slow motion of metastable patterns coexisting at the transition temperature.