01169nas a2200145   4500008004100000245008500041210006900126260001000195520065500205653006700860100002100927700001900948700002000967856003600987       2014                        en  d00aSecond Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional0 aSecond Order Asymptotic Development for the Anisotropic CahnHill  bSISSA3 aThe 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.10aGamma-convergence, Cahn-Hilliard functional, phase transitions1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni  uhttp://hdl.handle.net/1963/739001135nas a2200145   4500008004300000245008100043210006900124260002300193520065600216100002100872700002100893700001900914700002000933856003600953       2011                        en_Ud  00aSingular perturbation models in phase transitions for second order materials0 aSingular perturbation models in phase transitions for second ord  bIndiana University3 aA 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.1 aChermisi, Milena1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni  uhttp://hdl.handle.net/1963/3858