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 -