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# A New Formula for the Energy of Bulk Superconductivity

Published:2016-02-11
Printed: Sep 2016
• Ayman Kachmar,
Department of Mathematics, Lebanese University, Hadat, Lebanon
 Format: LaTeX MathJax PDF

## Abstract

The energy of a type II superconductor submitted to an external magnetic field of intensity close to the second critical field is given by the celebrated Abrikosov energy. If the external magnetic field is comparable to and below the second critical field, the energy is given by a reference function obtained as a special (thermodynamic) limit of a non-linear energy. In this note, we give a new formula for this reference energy. In particular, we obtain it as a special limit of a linear energy defined over configurations normalized in the $L^4$-norm.
 Keywords: Ginzburg-Landau functional Ginzburg-Landau functional
 MSC Classifications: 35B40 - Asymptotic behavior of solutions 35P15 - Estimation of eigenvalues, upper and lower bounds 35Q56 - Ginzburg-Landau equations

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