Ginzburg–Landau minimizers with prescribed degrees: dependence on domain

We study minimizers of the Ginzburg–Landau functional in an annular type domain with holes. We assume degrees 1 and ?1 on the boundary of the annulus, degree 0 on the boundaries of the holes. Two types of qualitatively different behavior of minimizers occur, depending on the value of the H¹-capacity of the domain. We also describe the asymptotic behavior of minimizers as the coherency length tends to ∞. To cite this article: L. Berlyand, P. Mironescu, C. R. Acad. Sci. Paris, Ser. I 337 (2003).