Lorentz Space Estimates for the Ginzburg-Landau Energy

Details Lorentz Space Estimates for the Ginzburg-Landau Energy Lorentz Space Estimates for the Ginzburg-Landau Energy

2007-05-08

arxiv.org/abs/0705.1094v1

Mathematics

Analysis of PDEs

52 pages, 1 figure

Scientific paper

In this paper we prove novel lower bounds for the Ginzburg-Landau energy with or without magnetic field. These bounds rely on an improvement of the "vortex balls construction" estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz space norm, on which it thus provides an upper bound. The Lorentz space $L^{2,\infty}$ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results.

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