Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field

Etienne Sandier; Sylvia Serfaty

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We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the $G L$ -energy $E_{ε}$ and the parameter $ε$ . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.

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