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On energy estimates for a Landau-Lifschitz type functional in higher dimensions

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The authors study the asymptotic behavior of radial minimizers of an energy functional associated with ferromagnets and antiferromagnets in higher dimensions. The location of the zeros of the radial minimizer is discussed. Moreover, several uniform estimates for the radial minimizer are presented. Based on these estimates, the authors establish global convergence of radial minimizers.

Abstract

The authors study the asymptotic behavior of radial minimizers of an energy functional associated with ferromagnets and antiferromagnets in higher dimensions. The location of the zeros of the radial minimizer is discussed. Moreover, several uniform estimates for the radial minimizer are presented. Based on these estimates, the authors establish global convergence of radial minimizers.

참고문헌 (8)

  1. F. Bethuel, "Ginzburg-Landau Vortices" (1994), Birkh¨auser
  2. M. Comte, "The behavior of a Ginzburg-Landau minimizer near its zeroes", Calc. Var. Partial Differential Equations, 4(4), pp.323~340 (1996)
  3. F. B. Hang, "Static theory for planar ferromagnets and antiferromagnets", Acta Math. Sin., 17(4), pp.541~580 (2001)
  4. Y. T. Lei, "Asymptotic behavior of the regularized minimizer of an energy functional in higher dimensions", J. Math. Anal. Appl., 334(2), pp.1341~1362 (2007)
  5. Y. T. Lei, "Some results on an n-Ginzburg-Landau-type minimizer", J. Comput. Appl. Math., 217(1), pp.123~136 (2008)
  6. P. Mironescu, "Une estimation pour les minimiseurs de l’´energie de Ginzburg-Landau", C. R. Acad. Sci. Paris Ser. I Math., 319(9), pp.941~943 (1994)
  7. N. Papanicolaou, "Semitopological solitons in planar ferromagnets", Nonlinearity, 12(2), pp.285~302 (1999)
  8. M. Struwe, "Une estimation asymptotique pour le mod´ele de Ginzburg-Landau", C. R. Acad. Sci. Paris Ser. I Math., 317(7), pp.677~680 (1993)

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