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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21960

De Lellis, C (2002). An example in the gradient theory of phase transitions. ESAIM: Control, Optimisation and Calculus of Variations, 7:285-289 (electronic).

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Abstract

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.

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7 citations in Web of Science®
6 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 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:08 Jan 2014 11:55
Publisher:EDP Sciences
ISSN:1262-3377
Publisher DOI:10.1051/cocv:2002012
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1925030

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