Accepted Paper

Inserted: 15 jul 2026
Last Updated: 18 jul 2026

Journal: Nonlinear Analysis
Year: 2026

Abstract:

We analyze fractional phase-transition energies with periodic heterogeneities at the critical $H^{1/2}$ scaling. We prove that the $\Gamma$-limit is a sharp-interface functional whose surface energy density combines homogenization and averaging effects. The resulting coefficient is a weighted combination of the minimum and the mean of the oscillatory parameter, reflecting the coexistence of multiple interaction scales. This behavior is specific to the critical regime and differs from the case $s>1/2$.

Keywords: nonlocal energies, fractional phase transitions