%0 Journal Article
%D 2014
%T Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%K Gamma-convergence, Cahn-Hilliard functional, phase transitions
%X 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.
%I SISSA
%G en
%U http://hdl.handle.net/1963/7390
%1 7439
%2 Mathematics
%4 1
%# MAT/05 ANALISI MATEMATICA
%$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-06-19T16:24:43Z
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%0 Journal Article
%J Indiana Univ. Math. J. 60 (2011) 367-409
%D 2011
%T Singular perturbation models in phase transitions for second order materials
%A Milena Chermisi
%A Gianni Dal Maso
%A Irene Fonseca
%A Giovanni Leoni
%X 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.
%B Indiana Univ. Math. J. 60 (2011) 367-409
%I Indiana University
%G en_US
%U http://hdl.handle.net/1963/3858
%1 851
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-27T10:47:12Z\\r\\nNo. of bitstreams: 1\\r\\nCheDMaFonLeo_2010.pdf: 350746 bytes, checksum: b384a4d0b82dd9713e1849ad3ef6a2be (MD5)
%R 10.1512/iumj.2011.60.4346
%0 Journal Article
%J Arch. Rational Mech. Anal. 183 (2007) 411-456
%D 2007
%T Surfactants in Foam Stability: A Phase-Field Model
%A Irene Fonseca
%A Massimiliano Morini
%A Valeriy Slastikov
%X The role of surfactants in stabilizing the formation of bubbles in foams is studied using a phase-field model. The analysis is centered on a van der Walls-Cahn-Hilliard-type energy with an added term accounting for the interplay between the presence of a surfactant density and the creation of interfaces. In particular, it is concluded that the surfactant segregates to the interfaces, and that the prescriptionof the distribution of surfactant will dictate the locus of interfaces, what is in agreement with experimentation.
%B Arch. Rational Mech. Anal. 183 (2007) 411-456
%G en_US
%U http://hdl.handle.net/1963/2035
%1 2161
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T15:51:40Z\\nNo. of bitstreams: 1\\n05-CNA-012.pdf: 414998 bytes, checksum: 3c44841388edba53080d531beadad798 (MD5)
%R 10.1007/s00205-006-0012-x