@article {2014,
title = {Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional},
year = {2014},
note = {This article is composed if 33 pages and recorded in PDF format},
publisher = {SISSA},
abstract = {The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.},
keywords = {Gamma-convergence, Cahn-Hilliard functional, phase transitions},
url = {http://hdl.handle.net/1963/7390},
author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni}
}
@article {2011,
title = {Singular perturbation models in phase transitions for second order materials},
journal = {Indiana Univ. Math. J. 60 (2011) 367-409},
number = {SISSA;20/2010/M},
year = {2011},
publisher = {Indiana University},
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 Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.},
doi = {10.1512/iumj.2011.60.4346},
url = {http://hdl.handle.net/1963/3858},
author = {Milena Chermisi and Gianni Dal Maso and Irene Fonseca and Giovanni Leoni}
}