Variational Problemson Multiply Connected Thin Strips II:Convergence of the GinzburgLandau
Abstract
Let M be a planar embedded graph whose arcs meet transversally at the vertices; Let ?(M) be a stripshaped domain around M, of width M except in a neighborhood of the singular points. Assume that the boundary of ?(M) is smooth. We consider the GinzburgLandau energy functional for superconductivity on ?(M). We prove that its minimizers converge in a suitable sense to the minimizers of a simpler functional on M. The supercurrents in ?(M) are shown to converge to onedimensional currents in M.
 Publication:

Archive for Rational Mechanics and Analysis
 Pub Date:
 2001
 DOI:
 10.1007/s002050100165
 Bibcode:
 2001ArRMA.160..309R