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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On a singular perturbation problem involving a ``circular-well'' potential


Authors: Nelly André and Itai Shafrir
Journal: Trans. Amer. Math. Soc. 359 (2007), 4729-4756
MSC (2000): Primary 35J20; Secondary 35B25, 35J60, 58E50
Published electronically: May 1, 2007
MathSciNet review: 2320649
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Abstract: We study the asymptotic behavior, as a small parameter $ \varepsilon$ goes to 0, of the minimizers for a variational problem which involves a ``circular-well'' potential, i.e., a potential vanishing on a closed smooth curve in $ \mathbb{R}^2$. We thus generalize previous results obtained for the special case of the Ginzburg-Landau potential.


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Additional Information

Nelly André
Affiliation: Département de Mathématiques, Université de Tours, 37200 Tours, France

Itai Shafrir
Affiliation: Department of Mathematics, Technion – Israel Institute of Technology, 32000 Haifa, Israel

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04344-9
PII: S 0002-9947(07)04344-9
Keywords: Singular perturbation, circular-well potential, Ginzburg-Landau energy
Received by editor(s): April 5, 2005
Published electronically: May 1, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.