@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} }