A variational model in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. In particular, the case where the scale ε of the small homogeneities is of the same order of the scale governing the phase transition is considered. The interaction between homogenization and the phase transitions process will lead, in the limit as ε → 0, to an anisotropic interfacial energy.

We would like to thank Will Feldman and Peter S. Morfe for pointing out the typo in the cell formula of Definition 1.3 in [1]. Here we present the correct formula for the energy density of the limiting functional, together with the minor modifications needed to adjust accordingly the proofs of the results presented in the paper.

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