UZH-Logo

An example in the gradient theory of phase transitions


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

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.

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.

Citations

7 citations in Web of Science®
6 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

24 downloads since deposited on 29 Nov 2010
14 downloads since 12 months
Detailed statistics

Additional indexing

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
Language:English
Date:2002
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:EDP Sciences
ISSN:1262-3377
Publisher DOI:10.1051/cocv:2002012
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1925030
Permanent URL: http://doi.org/10.5167/uzh-21960

Download

[img]
Preview
Filetype: PDF
Size: 121kB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations