An example in the gradient theory of phase transitions

Camillo De Lellis
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Submission date: 08. Apr. 2002
Pages: 8
published in: Control, optimisation and calculus of variations, 7 (2002), p. 285-289 (electronic) 
MSC-Numbers: 49J45, 74G65, 76M30
Keywords and phrases: phase transitions, gamma-convergence, asymptotic analysis, singular perturbations, ginzburg--landau
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Abstract:
We prove by giving an example that when the asymptotic behavior of functionals is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case is no longer true in higher dimensions.