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arXiv · 2604.12689

Homogenization in one-dimensional higher-order non-local models of phase transitions

Fabrizio Caragiulo·Sergio Scalabrino·Edoardo Voglino
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Abstract

We study the limit behavior of Cahn--Hilliard-type functionals in which the derivative is replaced by higher-order fractional derivatives and modulated by an oscillating factor. Depending on the ratio between the oscillation scale and the interface length, we identify three different regimes and prove $\Gamma$-convergence in each regime to a suitable sharp-interface limit functional. In the extreme regimes, we prove a separation-of-scales effect that enables us to highlight the difference relative to the local models.

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Fabrizio Caragiulo, Sergio Scalabrino, Edoardo Voglino. 2026-04-14. Homogenization in one-dimensional higher-order non-local models of phase transitions. https://doi.org/10.1007/s11587-026-01131-7

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