Static Theory for Planar Ferromagnets and Antiferromagnets

Acta Mathematica Sinica, English Series

Volumn 17, Issue 4, 2001, Pages 541-580

  Hang, Feng Bo ^a,b   Lin, Fang Hua ^a  

^a NEW YORK UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Ginzburg Landau type equations; Gradient estimate; Minimizing harmonic maps; Quantization; Radial solutions; Stability; Vortices

Indexed keywords

EID: 0346526180     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101140100136     Document Type: Article

References (22)

1. S. Komineas, N. Papanicolaou, Topology and dynamics in ferromagnetic media, Phys. D., 1996, 99(1): 81-107.
2. S. Komineas, N. Papanicolaou, Vortex dynamics in two-dimensional antiferromagnets, Nonlinearity, 1998, 11(2): 265-290.
3. A. P. Malozemoff, J. C. Slonczewski, Magnetic domain walls in bubble materials, New York: Wiley, 1981.
4. N. Papanicolaou, P. N. Spathis, Semitopological solitons in planar ferromagnets, Nonlinearity, 1999, 12(2): 285-302.
5. F. Bethuel, H. Brezis, F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calc. Var. and PDE., 1993, 1(3): 123-148.
6. F. Bethuel, H. Brezis, F. Hélein, Ginzburg-Landau vortices, Boston: Birkhäuser, 1994.
7. F. H. Lin, Static and moving vortices in Ginzburg-Landau theories, Nonlinear Partial Differential Equations in Geometry and Physics (Knoxville, TN, 1995), Basel: Birkhäuser, 1997, 71-111.
8. F. H. Lin, Some dynamical properties of Ginzburg-Landau vortices, Comm. Pure Appl. Math., 1996, 49(4): 323-359.
9. P. Mironescu, On the stability of radial solutions of the Ginzburg-Landau equation, J. Func. Anal., 1995, 130(2): 334-344.
10. 2, Arch. Rat. Mech. Anal., 1994, 126(1): 35-58.
11. F. B. Hang, F. H. Lin, Minimizing p-harmonic maps, in press.
12. C. B. Morrey, Jr., Multiple integrals in the calculus of variations, Berlin-Heidelberg-New York: Springer-Verlag, 1966.
13. F. Hélein, Régularité des applications faiblement harmoniques entre une surface et une varitée Riemannienne, C.R. Acad. Sci. Paris Sér. I Math., 1991, 312(8): 591-596.
14. J. Qing, Boundary regularity of weakly harmonic maps from surfaces, J. Func. Anal., 1993, 114(2): 458-466.
15. D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, 2nd edition, 3rd printing, Berlin: Springer-Verlag, 1998.
16. Y. L. Xin, Geometry of harmonic maps, Boston: Birkhäuser, 1996.
17. R. Schoen, S. T. Yau, Lectures on harmonic maps, Cambridge: International Press, 1997.
18. M. Struwe, On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions, Diff. Integ. Eq., 1994, 7(6): 1613-1624.
19. M. Struwe, Erratum to [18], Diff. Integ. Eq., 1995, 8(1): 224.
20. P. Baird, Harmonic maps with symmetry, harmonic morphisms and deformations of metrics, Boston: Pitman, 1983.
21. X. Chen, C. M. Elliott, T. Qi, Shooting method for vortex solutions of a complex-valued Ginzburg-Landau equation, Proc. Roy. Soc. Edinburgh, Sec. A Math., 1994, 124(6): 1075-1088.
22. P. Hagan, Spiral waves in reaction diffusion equations, SIAM J. Appl. Math., 1982, 42(4): 762-786.