TY - JOUR
T1 - Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional
Y1 - 2014
A1 - Gianni Dal Maso
A1 - Irene Fonseca
A1 - Giovanni Leoni
KW - Gamma-convergence, Cahn-Hilliard functional, phase transitions
AB - 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.
PB - SISSA
UR - http://hdl.handle.net/1963/7390
N1 - This article is composed if 33 pages and recorded in PDF format
U1 - 7439
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -
TY - JOUR
T1 - Singular perturbation models in phase transitions for second order materials
JF - Indiana Univ. Math. J. 60 (2011) 367-409
Y1 - 2011
A1 - Milena Chermisi
A1 - Gianni Dal Maso
A1 - Irene Fonseca
A1 - Giovanni Leoni
AB - 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.
PB - Indiana University
UR - http://hdl.handle.net/1963/3858
U1 - 851
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -