Variational Problemson Multiply Connected Thin Strips II:Convergence of the Ginzburg-Landau
Abstract
Let M be a planar embedded graph whose arcs meet transversally at the vertices; Let ?(M) be a strip-shaped 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 Ginzburg-Landau 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 one-dimensional currents in M.
- Publication:
-
Archive for Rational Mechanics and Analysis
- Pub Date:
- 2001
- DOI:
- 10.1007/s002050100165
- Bibcode:
- 2001ArRMA.160..309R