Variational Problems¶on Multiply Connected Thin Strips II:¶Convergence of the Ginzburg-Landau
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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.
KeywordsSingular Point Variational Problem Thin Strip Suitable Sense Embed Graph
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