| Abstract: |
| We investigate the Cahn--Hilliard functional, a prototypical model for liquid--liquid phase separation, in a highly irregular setting. In particular, we consider potentials of low regularity that vanish on space-dependent wells. Under very mild assumptions, we prove a robust compactness result. By slightly strengthening the regularity of the wells and the growth conditions of the potential near them, we then fully characterize the asymptotic behavior of the associated family of functionals via a $\Gamma$-convergence analysis. |
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