Ginzburg–Landau minimizers with prescribed degrees: dependence on domain
Leonid V. Berlyand, Petru Mironescu · Comptes Rendus Mathématique · 2003
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 H 1 -capacity of the domain. We also describe the asymptotic behavior of minimizers as the coherency length tends to ∞.