The gradient theory of phase transitions for systems with two potential wells

Abstract

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.