THE GINZBURG–LANDAU FUNCTIONAL WITH A DISCONTINUOUS AND RAPIDLY OSCILLATING PINNING TERM. PART I: THE ZERO DEGREE CASE
Mickaël Dos Santos, Petru Mironescu, Oleksandr Misiats · Communications in Contemporary Mathematics · 2011
We consider minimizers of the Ginzburg–Landau energy with pinning term and zero degree Dirichlet boundary condition. Without any assumptions on the pinning term, we prove that these minimizers do not develop vortices in the limit ε → 0. We next consider the specific case of a periodic discontinuous pinning term taking two values. In this setting, we determine the asymptotic behavior of the minimizers as ε → 0.