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An example in the gradient theory of phase transitions

Published online by Cambridge University Press:  15 September 2002

Camillo De Lellis
Camillo De Lellis*
Affiliation:
Scuola Normale Superiore, P.zza dei Cavalieri 7, 56100 Pisa, Italy; delellis@cibs.sns.it.
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Abstract

We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals $\int_\Omega \varepsilon|\nabla^2 u|^2+(1-|\nabla u|^2)^2/\varepsilon$ 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 (see [2]) is no longer true in higher dimensions.

Keywords

Phase transitionsΓ-convergenceasymptotic analysissingular perturbationGinzburg–Landau.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002 , pp. 285 - 289
Copyright
© EDP Sciences, SMAI, 2002

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References

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