preprint

Inserted: 16 jul 2025
Last Updated: 16 jul 2025

Year: 2025

Abstract:

We study functionals $ F_\varepsilon (u) := \lambda_\varepsilon \int_\Omega W(u) \, dx + \varepsilon \mid u \mid_{H^{1/2}}^2$ for a double well potential $W$ and the Gagliardo seminorm $\mid \cdot\mid_{H^{1/2}}$ when $\varepsilon \ln(\lambda_\varepsilon) \rightarrow k$ as $\varepsilon \rightarrow 0^+$ and show compactness in the space of $BV$ functions on $\Omega$ and the $\Gamma$-convergence to the classical surface tension functional.