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Journal Articles Communications in Partial Differential Equations Year : 2017

Asymptotic behavior of critical points of an energy involving a loop-well potential

Abstract

We describe the asymptotic behavior of critical points of $\int_\Omega [|\nabla u|^2+W(u)/\varepsilon^2]$ when $\varepsilon\to 0$. Here, $W$ is a Ginzburg-Landau type potential, vanishing on a simple closed curve $\Gamma$. Unlike the case of the standard Ginzburg-Landau potential $W(u) = (1 − |u|^2)^2/4$, studied by Bethuel, Brezis and Hélein, we do not assume any symmetry on $W$ or $\Gamma$. In order to overcome the difficulties due to the lack of symmetry, we develop new tools which might be of independent interest.
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Dates and versions

hal-01532476 , version 1 (02-06-2017)
hal-01532476 , version 2 (12-06-2017)
hal-01532476 , version 3 (27-09-2017)

Identifiers

  • HAL Id : hal-01532476 , version 3

Cite

Petru Mironescu, Itai Shafrir. Asymptotic behavior of critical points of an energy involving a loop-well potential. Communications in Partial Differential Equations, 2017, 42 (12), pp.1837-1870. ⟨hal-01532476v3⟩
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