Asymptotic analysis of second order nonlocal Cahn-Hilliard-type functionals

Dal Maso, Gianni; Fonseca, Irene; Leoni, Giovanni

doi:10.1090/tran/7151

Asymptotic analysis of second order nonlocal Cahn-Hilliard-type functionals
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by Gianni Dal Maso, Irene Fonseca and Giovanni Leoni PDF

Trans. Amer. Math. Soc. 370 (2018), 2785-2823 Request permission

Abstract:

In this paper the study of a nonlocal second order Cahn–Hilliard-type singularly perturbed family of functions is undertaken. The kernels considered include those leading to Gagliardo fractional seminorms for gradients. Using $\Gamma$ convergence the integral representation of the limit energy is characterized leading to an anisotropic surface energy on interfaces separating different phases.

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