Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 14-CNA-019 Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional Gianni Dal Maso SISSA Via Bonomea 265 34136 Trieste, Italy Irene Fonseca Department of Mathematical Sciences Carnegie Mellon University Pittsburgh PA 15213-3890 USA Giovanni Leoni Department of Mathematical Sciences Carnegie Mellon University Pittsburgh PA 15213-3890 USA Abstract: The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\epsilon$ 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. Get the paper in its entirety as Back to CNA Publications