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

Published online by Cambridge University Press:  14 November 2011

Irene Fonseca  and
Luc Tartar
Irene Fonseca
Affiliation:
Department of Mathematics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, U.S.A.
Luc Tartar
Affiliation:
Department of Mathematics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, U.S.A.
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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:RN→R supports two phases and N ≧1. We obtain the Γ(L1(Ω))-limit of the sequence

Moreover, we improve a compactness result ensuring the existence of a subsequence of minimisers of Eε(·) converging in L1(Ω) to a minimiser of E0(·) with minimal interfacial area.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 1-2 , 1989 , pp. 89 - 102
Copyright
Copyright © Royal Society of Edinburgh 1989

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