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De Lellis, C (2002). An example in the gradient theory of phase transitions. ESAIM: Control, Optimisation and Calculus of Variations, 7:285-289 (electronic).
We prove by giving an example that when n ≥ 3 the asymptotic behavior of functionals ∫Ω[ε|∇2u|2+(1−|∇u|2)2/ε] 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 Aviles and Giga 1987) is no longer true in higher dimensions.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Control and Systems Engineering
Physical Sciences > Control and Optimization Physical Sciences > Computational Mathematics |
| Uncontrolled Keywords: | phase transitions, Γ-convergence, asymptotic analysis, singular perturbation, Ginzburg-Landau energy |
| Language: | English |
| Date: | 2002 |
| Deposited On: | 29 Nov 2010 16:27 |
| Last Modified: | 03 Sep 2024 01:37 |
| Publisher: | EDP Sciences |
| ISSN: | 1262-3377 |
| OA Status: | Hybrid |
| Publisher DOI: | https://doi.org/10.1051/cocv:2002012 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1925030 |
De Lellis, C