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

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dc.creatorTice, Ian
dc.date2007-05-08
dc.date.accessioned2026-07-07T08:00:01Z
dc.date.available2026-07-07T08:00:01Z
dc.descriptionIn this paper we continue the study of Lorentz space estimates for the Ginzburg-Landau energy started in our previous paper, \cite{p1}. 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 $L^{2,\infty}$ Lorentz space norm of $\nabla_A u$. We also establish convergence of the gauge-invariant Jacobians (vorticity measures) in the dual of a function space defined in terms of Lorentz spaces.
dc.description58 pages
dc.identifierhttps://arxiv.org/abs/0705.1114
dc.identifierhttp://arxiv.org/abs/0705.1114
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128584
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35J50, 46E30, 58E50, 82D55
dc.titleLorentz Space Estimates and Jacobian Convergence for the Ginzburg-Landau Energy with Applied Magnetic Field
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