# Singular perturbation models in phase transitions for second order materials

created by chermisi on 17 Mar 2010
modified by dalmaso on 19 Jul 2013

[BibTeX]

Published Paper

Inserted: 17 mar 2010
Last Updated: 19 jul 2013

Journal: Indiana University Mathematics Journal
Volume: 60
Pages: 367-410
Year: 2011

Abstract:

A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies $F_\varepsilon$ having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of $\{F_{\varepsilon}\}$ is studied using $\Gamma$-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.