Synopsis In this paper we generalise the gradient theory of phase transitions to the vector valued case. We consider the family of perturbations of the nonconvex functional where W:R N →R supports two phases and N ≧1 . We obtain the Γ( L 1 (Ω))-limit of the sequence Moreover, we improve a compactness result ensuring the existence of a subsequence of minimisers of E ε (·) converging in L 1 (Ω) to a minimiser of E 0 (·) with minimal interfacial area.
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Fonseca et al. (1989) studied this question.
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