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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On a singular perturbation problem involving a “circular-well” potential
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by Nelly André and Itai Shafrir PDF
Trans. Amer. Math. Soc. 359 (2007), 4729-4756 Request permission

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
  • Received by editor(s): April 5, 2005
  • Published electronically: May 1, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2320649