The ground state energy of the two dimensional Ginzburg–Landau functional with variable magnetic field
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 2, pp. 325-345.

We consider the Ginzburg–Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. We determine an accurate asymptotic formula for the minimizing energy when the Ginzburg–Landau parameter and the magnetic field are large and of the same order. As a consequence, it is shown how bulk superconductivity decreases in average as the applied magnetic field increases.

DOI : 10.1016/j.anihpc.2013.12.002
Classification : 82D55
Mots-clés : Superconductivity, Ginzburg–Landau, Variable magnetic field 
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     author = {Attar, K.},
     title = {The ground state energy of the two dimensional {Ginzburg{\textendash}Landau} functional with variable magnetic field},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {325--345},
     publisher = {Elsevier},
     volume = {32},
     number = {2},
     year = {2015},
     doi = {10.1016/j.anihpc.2013.12.002},
     mrnumber = {3325240},
     zbl = {1320.82071},
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     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.12.002/}
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Attar, K. The ground state energy of the two dimensional Ginzburg–Landau functional with variable magnetic field. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 2, pp. 325-345. doi : 10.1016/j.anihpc.2013.12.002. http://www.numdam.org/articles/10.1016/j.anihpc.2013.12.002/

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