Variational problems on multiply connected thin strips. III: Integration of the Ginzburg-Landau equations over graphs (Q2723470)

The authors in their earlier paper [Variational problems on multiply connected thin strips. II: Convergence of the Ginzburg-Landau functional. Technical Report 294, UMR 5585 CNRS Equipe d'Analyse Numérique, April 1999] have shown that the Ginzburg-Landau (GL) functional of superconductivity in 2D on a thin set can be approximated by 1D GL on a graph. In this work they investigate minimizers of the GL functional and the associated Euler-Lagrange equation on a general graph embedded in the plane. The authors prove that the problem under consideration depends only on the fluxes of the applied magnetic field through the regions bordered by the structure related to the graph.