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 16-CNA-024 Asymptotic Analysis of Second Order Nonlocal Cahn-Hilliard-Type Functionals Gianni Dal MasoSISSA Trieste, Italy dalmaso@sissa.it Irene FonsecaDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213fonseca@andrew.cmu.edu Giovanni LeoniDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213giovanni@andrew.cmu.eduAbstract: 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.Get the paper in its entirety as  16-CNA-024.pdf