$\Gamma$-convergence for nonlocal phase transitions involving the $H^{1/2}$ norm and surfactants

Giuliana Fusco, Tim Heilmann

We study functionals \begin{equation*} F_\varepsilon (u,ρ) := \frac{1}{\varepsilon} \int_ΩW(u) \, dx + \frac{1}{|\ln(\varepsilon)|} \int_Ω\int_Ω \frac{(u(y) - u(x))^2}{|y - x|^{N+1…