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arXiv · 2410.19624

Nonlocal Phase Transitions with Singular Heterogeneous Kernels

Wes Caldwell
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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. 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.

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Wes Caldwell. 2024-10-25. Nonlocal Phase Transitions with Singular Heterogeneous Kernels. https://arxiv.org/abs/2410.19624

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