2007/05/08 by Sylvia Serfaty, Ian Tice, Serfaty, Sylvia +1
Mathematics · Physics and Astronomy · #35J50 #58E50 #82D55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35J50 #msc:58E50 #msc:82D55
paper · pdf · doi:10.48550/arxiv.0705.1094
52 pages, 1 figure
arxiv created 2007/05/08 · arxiv updated 2009/12/01
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 L2,∞ 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.