| Title | An example in the gradient theory of phase transitions. |
| Publication Type | Journal Article |
| Year of Publication | 2002 |
| Authors | De Lellis C. |
| Journal | ESAIM: Control, Optimisation and Calculus of Variations |
| Volume | 7 |
| Pagination | 285–289 (electronic) |
| Publisher | EDP Sciences |
| Type of Article | phase |
| ISSN | 1262-3377 |
| Keywords | asymptotic analysis, Ginzburg-Landau energy, phase transitions, singular perturbation, \ensuremathΓ-convergence |
| Abstract | We prove by giving an example that when n ? 3 the asymptotic behavior of functionals $\int$?[\ensuremathε\ensuremath|?2u\ensuremath|2+(1?\ensuremath|?u\ensuremath|2)2/\ensuremathε] 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. |
| Notes | ESAIM Control Optim. Calc. Var. 7 (2002), 285–289 |
| URL | https://www.esaim-cocv.org/articles/cocv/abs/2002/01/cocvVol7-12/cocvVol7-12.html |
| DOI | 10.1051/cocv:2002012 |
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