2024/10/25 by Caldwell, Wes
Mathematics · #Differential Equations and Numerical Methods #Differential Equations and Boundary Problems #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2410.19624
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. The kernels considered include those leading to Gagliardo seminorms for fractional Sobolev spaces. The limit energy is computed via Γ-convergence and shown to be an anisotropic surface energy on the interface between the two phases.