preprint

Inserted: 11 nov 2026

Year: 2026

Abstract:

We study $Γ$-convergence, under appropriate scalings, of the energy functionals \[ F_\varepsilon(u) := [u]_{H^s(Q)}^2 + \int_{Q} W_\varepsilon(u)\,dx, \] where $s \in (0,1)$, $[\cdot]_{H^s(Q)}$ denotes the $H^s$-seminorm in $Q\subset \mathbb{R}^{n}$, and $W_\varepsilon$ is a multi-well potential featuring infinitely many equally spaced wells together with additional intermediate wells whose height vanishes at a prescribed rate. Depending on this rate, different limiting behaviors emerge, ranging from classical models to new intermediate regimes.