On a singular perturbation problem involving a “circular-well” potential

André, Nelly; Shafrir, Itai

doi:10.1090/S0002-9947-07-04344-9

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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