| Issue |
ESAIM: COCV
Volume 7, 2002
|
|
|---|---|---|
| Page(s) | 285 - 289 | |
| DOI | https://doi.org/10.1051/cocv:2002012 | |
| Published online | 15 September 2002 | |
An example in the gradient theory of phase transitions
Scuola Normale Superiore,
P.zza dei Cavalieri 7,
56100 Pisa, Italy;
delellis@cibs.sns.it.
Received:
4
December
2001
We prove by giving an example that when n ≥ 3 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 (see [2]) is no longer true in higher dimensions.
Mathematics Subject Classification: 49J45 / 74G65 / 76M30
Key words: Phase transitions / Γ-convergence / asymptotic analysis / singular perturbation / Ginzburg–Landau.
© EDP Sciences, SMAI, 2002
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