Lorentz space estimates for the Ginzburg-Landau energy |
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Authors: | Sylvia Serfaty Ian Tice |
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Institution: | Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012, USA |
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Abstract: | 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. |
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Keywords: | Ginzburg-Landau Vortex balls Ball construction Lorentz spaces Best regards Sylvia Serfaty |
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