Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON ENERGY ESTIMATES FOR A LANDAU-LIFSCHITZ TYPE FUNCTIONAL IN HIGHER DIMENSIONS

  • Qi, Longxing (INSTITUTE OF MATHEMATICS SCHOOL OF MATHEMATICS AND COMPUTER SCIENCE NANJING NORMAL UNIVERSITY) ;
  • Lei, Yutian (INSTITUTE OF MATHEMATICS SCHOOL OF MATHEMATICS AND COMPUTER SCIENCE NANJING NORMAL UNIVERSITY)
  • Published : 2009.11.01
Download PDF
⟨ Previous Next ⟩

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.

Keywords

References

  1. F. Bethuel, H. Brezis, and F. Helein, Ginzburg-Landau Vortices, Birkhauser, Berlin, 1994.
  2. M. Comte and P. Mironescu, The behavior of a Ginzburg-Landau minimizer near its zeroes, Calc. Var. Partial Differential Equations 4 (1996), no. 4, 323-340. https://doi.org/10.1007/BF01190822
  3. F. B. Hang and F. H. Lin, Static theory for planar ferromagnets and antiferromagnets, Acta Math. Sin. (Engl. Ser.) 17 (2001), no. 4, 541-580. https://doi.org/10.1007/s101140100136
  4. Y. T. Lei, Asymptotic behavior of the regularized minimizer of an energy functional in higher dimensions, J. Math. Anal. Appl. 334 (2007), no. 2, 1341-1362. https://doi.org/10.1016/j.jmaa.2007.01.006
  5. Y. T. Lei, Some results on an n-Ginzburg-Landau-type minimizer, J. Comput. Appl. Math. 217 (2008), no. 1, 123-136. https://doi.org/10.1016/j.cam.2007.06.021
  6. P. Mironescu, Une estimation pour les minimiseurs de lenergie de Ginzburg-Landau, C. R. Acad. Sci. Paris Ser. I Math. 319 (1994), no. 9, 941-943.
  7. N. Papanicolaou and P. N. Spathis, Semitopological solitons in planar ferromagnets, Nonlinearity 12 (1999), no. 2, 285-302. https://doi.org/10.1088/0951-7715/12/2/008
  8. M. Struwe, Une estimation asymptotique pour le modele de Ginzburg-Landau, C. R. Acad. Sci. Paris Ser. I Math. 317 (1993), no. 7, 677-680.