Publication 24-CNA-015

Nonlocal Phase Transitions with Singular Heterogeneous Kernels

Wes Caldwell
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
wcaldwell@cmu.edu

Abstract: In this paper the study of a non-local Cahn-Hilliard-type singularly perturbed family of functionals is undertaken, generalizing known results by Alberti & Bellettini [2]. The kernels considered include those leading to Gagliardo seminorms for fractional Sobolev spaces. The limit energy is computed via $\Gamma$-convergence and shown to be an anisotropic surface energy on the interface between the two phases.

Get the paper in its entirety as  24-CNA-015.pdf

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