Lorentz Space Estimates and Jacobian Convergence for the Ginzburg-Landau Energy with Applied Magnetic Field

2007/05/08 by Ian Tice, Tice, Ian
Mathematics · Physics and Astronomy · #35J50 #46E30 #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:46E30 #msc:58E50 #msc:82D55

paper · pdf · doi:10.48550/arxiv.0705.1114

58 pages

arxiv created 2007/05/08 · arxiv updated 2009/12/01

Abstract

In this paper we continue the study of Lorentz space estimates for the Ginzburg-Landau energy started in our previous paper, \citep1. We focus on getting estimates for the Ginzburg-Landau energy with external magnetic field h_ex in certain interesting regimes of h_ex. This allows us to show that for configurations close to minimizers or local minimizers of the energy, the vorticity mass of the configuration (u,A) is comparable to the L^2,∞ Lorentz space norm of ∇_A u. We also establish convergence of the gauge-invariant Jacobians (vorticity measures) in the dual of a function space defined in terms of Lorentz spaces.

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