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.
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 Oct 2023 01:40 |
| 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