The ground state energy of the three dimensional Ginzburg-Landau functional. Part I: Bulk regime

Details The ground state energy of the three dimensional Ginzburg-Landau functional. Part I: Bulk regime The ground state energy of the three dimensional Ginzburg-Landau functional. Part I: Bulk regime

2011-09-06

arxiv.org/abs/1109.1287v1

Mathematics

Analysis of PDEs

36 pages

Scientific paper

We consider the Ginzburg-Landau functional defined over a bounded and smooth three dimensional domain. Supposing that the magnetic field is comparable with the second critical field and that the Ginzburg-Landau parameter is large, we determine a sharp asymptotic estimate of the minimizing energy. In particular, this shows how bulk superconductivity decreases in average as the applied magnetic field approaches the second critical field from below. Other estimates are also obtained which allow us to obtain, in a subsequent paper, a fine characterization of the second critical field. The approach relies on a careful analysis of several limiting energies, which is of independent interest.

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