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Energy asymptotics for type II superconductors. (English) Zbl 1160.82365
Summary: We study the Ginzburg-Landau functional in the parameter regime describing ‘Type II superconductors’. In the exact regime considered minimizers are localized to the boundary-i.e. the sample is only superconducting in the boundary region. Depending on the relative size of different parameters we describe the concentration behavior and give leading order energy asymptotics. This generalizes previous results by K. Lu and X.-B. Pan [Physica D 127, No. 1–2, 73–104 (1999; Zbl 0934.35174)], the second author and Pan [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 20, No. 1, 145–181 (2003; Zbl 1060.35132)], and Pan [Calc. Var. Partial Differ. Equ. 14, No. 4, 447–482 (2002; Zbl 1006.35090)].

MSC:
82D55 Statistical mechanics of superconductors
35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
35J50 Variational methods for elliptic systems
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
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