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
DOI:
https://doi.org/10.1090/S0002-9947-07-04344-9
Published electronically:
May 1, 2007
MathSciNet review:
2320649
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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.
