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

Abstract

We study the asymptotic behavior, as a small parameter ε \varepsilon goes to 0 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 R 2 \mathbb {R}^2 . We thus generalize previous results obtained for the special case of the Ginzburg-Landau potential.