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

Abstract

ABSTRACTWe describe the asymptotic behavior of critical points of when 𝜀→0. Here, W is a Ginzburg–Landau-type potential, vanishing on a simple closed curve Γ. Unlike the case of the standard Ginzburg–Landau potential , studied by Bethuel, Brezis and Hélein, we do not assume any symmetry on W or Γ. To overcome the difficulties due to the lack of symmetry, we develop new tools which might be of independent interest.