An example in the gradient theory of phase transitions
Scuola Normale Superiore,
P.zza dei Cavalieri 7,
56100 Pisa, Italy;
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 ) 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