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/1963/7390