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Zbl pre05024486
Alama, Stan; Bronsard, Lia; Montero, J.Alberto
On the Ginzburg--Landau model of a superconducting ball in a uniform field. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 23, No. 2, 237-267 (2006). ISSN 0294-1449

Summary: We consider the three-dimensional Ginzburg--Landau model for a solid spherical superconductor in a uniform magnetic field, in the limit as the Ginzburg--Landau parameter $\kappa=1/ \epsilon \rightarrow \infty$. By studying a limiting functional we identify a candidate for the lower critical field $H_{c_{1}}$, the value of the applied field strength at which minimizers first exhibit vortices. For applied fields of this strength we show the existence of locally minimizing solutions with vortices located along a diameter of the sphere parallel to the applied field direction. To analyze these problems we use a combination of techniques, involving least perimeter problems, weak Jacobians and rectifiable currents, and special Hodge decompositions.

MSC 2000:: *35J50 Systems of elliptic equations, variational methods
35B25 Singular perturbations (PDE)

Keywords: calculus of variations; elliptic partial differential equations; rectifiable currents; superconductivity

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