Local minimizers with vortices to the Ginzburg‐Landau system in three dimensions
José Alberto Montero, Peter Sternberg, William P. Ziemer · Communications on Pure and Applied Mathematics · 2003
Abstract We construct local minimizers to the Ginzburg‐Landau energy in certain three‐dimensional domains based on the asymptotic connection between the energy and the total length of vortices using the theory of weak Jacobians. Whenever there exists a collection of locally minimal line segments spanning the domain, we can find local minimizers with arbitrarily assigned degrees with respect to each segment. © 2003 Wiley Periodicals, Inc.