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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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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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Dewey Decimal Classification:||510 Mathematics|
|Uncontrolled Keywords:||phase transitions; Γ-convergence; asymptotic analysis; singular perturbation; Ginzburg-Landau energy|
|Deposited On:||29 Nov 2010 16:27|
|Last Modified:||08 Jan 2014 11:55|
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