The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part I: the zero degree case

Mickaël dos Santos (1) , Petru Mironescu (1) , Oleksandr Misiats (2)

1 ICJ - Institut Camille Jordan
2 Department of Mathematics

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 $\varepsilon\to0$. 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 $\varepsilon\to0$.

Domaines: Equations aux dérivées partielles [math.AP]

Mickaël dos Santos, Petru Mironescu, Oleksandr Misiats. The Ginzburg-Landau functional with a discontinuous and rapidly oscillating pinning term. Part I: the zero degree case. Commun. Contemp. Math., 2011, 13 (5), pp.885-914. ⟨hal-00515893⟩