TitleAn example in the gradient theory of phase transitions.
Publication TypeJournal Article
Year of Publication2002
AuthorsDe Lellis C.
JournalESAIM: Control, Optimisation and Calculus of Variations
Volume7
Pagination285–289 (electronic)
PublisherEDP Sciences
Type of Articlephase
ISSN1262-3377
Keywordsasymptotic 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

URLhttps://www.esaim-cocv.org/articles/cocv/abs/2002/01/cocvVol7-12/cocvVol7-12.html
DOI10.1051/cocv:2002012
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