A Gamma-convergence result for the two-gradient theory of phase transitions

Sergio Conti, Irene Fonseca, and Giovanni Leoni

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Submission date: 26. Jun. 2001 (revised version: January 2002)
Pages: 61
published in: Communications on pure and applied mathematics, 55 (2002) 7, p. 857-936 
DOI number (of the published article): 10.1002/cpa.10035
Bibtex
MSC-Numbers: 35G99, 35M99, 49J40, 49J45, 49K20, 74B20, 74G65, 74N99
Keywords and phrases: phase transition, double-well potential, singular perturbations, gamma-convergence, vertical matching, lateral matching
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Abstract:
The generalization to gradient vector fields of the classical double-well, singularly perturbed functionals,

where if and only if or , and is a rank-one matrix, is considered. Under suitable constitutive and growth hypotheses on W it is shown that -converge to

where is the (constant) interfacial energy per unit area.Accepted for publication in Communications in Pure and Applied Mathematics, copyright © John Wiley & Sons, Inc. 2002