01135nas 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