Pinning phenomena in the Ginzburg-Landau model of superconductivity

We study the Ginzburg-Landau energy of superconductors with a term a, model ling the pinning of vortices by impurities in the limit of a large Ginzburg -Landau parameter kappa = 1/epsilon, The function a(epsilon) is oscillating between 1/2 and 1 with a scale which may tend to 0 as K tends to infinity. Our aim is to understand that in the large K limit, stable configurations s hould correspond to vortices pinned at the minimum of a(epsilon) and to der ive the limiting homogenized free-boundary problem which arises for the mag netic field in replacement of the London equation. The method and technique s that we use are inspired from those of Sandier and Serfaty, Annales Scien tifiques de l'ENS (to appear) (in which the case a(epsilon) = 1 was treated ) and based on energy estimates, convergence of measures and construction o f approximate solutions. Because of the term a(epsilon)(x) in the equations , we also need homogenization theory to describe the fact that the impuriti es, hence the vortices, form a homogenized medium in the material. (C) 2001 Editions scientifiques et medicales Elsevier SAS.