The gradient flow motion of boundary vortices

 Access to full text

 Full (PDF)

1. [1] Alberti G., Baldo S., Orlandi G., Variational convergence for functionals of Ginzburg–Landau type, Indiana Univ. Math. J.54 (2005) 1411-1472. Zbl1160.35013
2. [2] Alberti G., Bouchitté G., Seppecher P., Un résultat de perturbations singulières avec la norme $H^{1/2}$, C. R. Acad. Sci. Paris Sér. I Math.319 (4) (1994) 333-338. Zbl0845.49008MR1289307
3. [3] Alberti G., Bouchitté G., Seppecher P., Phase transition with the line-tension effect, Arch. Rational Mech. Anal.144 (1) (1998) 1-46. Zbl0915.76093MR1657316
4. [4] Almeida L., Bethuel F., Topological methods for the Ginzburg–Landau equations, J. Math. Pures Appl. (9)77 (1) (1998) 1-49. Zbl0904.35023
5. [5] Bethuel F., Brezis H., Hélein F., Ginzburg–Landau Vortices, Progress in Nonlinear Differential Equations and their Applications, vol. 13, Birkhäuser Boston Inc., Boston, MA, 1994. Zbl0802.35142
6. [6] X. Cabré, N. Cónsul, Minimizers for boundary reactions: renormalized energy, location of singularities, and applications, in preparation. 
7. [7] Cabré X., Solà-Morales J., Layer solutions in a half-space for boundary reactions, Comm. Pure Appl. Math.58 (12) (2005) 1678-1732. Zbl1102.35034MR2177165
8. [8] Carbou G., Thin layers in micromagnetism, Math. Models Methods Appl. Sci.11 (9) (2001) 1529-1546. Zbl1012.82031MR1872680
9. [9] DeSimone A., Kohn R.V., Müller S., Otto F., A reduced theory for thin-film micromagnetics, Comm. Pure Appl. Math.55 (11) (2002) 1408-1460. Zbl1027.82042MR1916988
10. [10] Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. Zbl0804.28001MR1158660
11. [11] A. Garroni, S. Müller, A variational model for dislocations in the line-tension limit, Preprint 76, Max Planck Institute for Mathematics in the Sciences, 2004. Zbl1158.74365
12. [12] Gioia G., James R.D., Micromagnetics of very thin films, Proc. Roy. Soc. London Ser. A453 (1997) 213-223. 
13. [13] Jerrard R.L., Soner H.M., Dynamics of Ginzburg–Landau vortices, Arch. Rational Mech. Anal.142 (2) (1998) 99-125. Zbl0923.35167
14. [14] Kohn R.V., Slastikov V.V., Another thin-film limit of micromagnetics, Arch. Rational Mech. Anal.178 (2) (2005) 227-245. Zbl1074.78012MR2186425
15. [15] Kohn R.V., Slastikov V.V., Effective dynamics for ferromagnetic thin films: a rigorous justification, Proc. Roy. Soc. London Ser. A Math. Phys. Eng. Sci.461 (2053) (2005) 143-154. Zbl1145.82358MR2124197
16. [16] Kurzke M., Boundary vortices in thin magnetic films, Calc. Var. Partial Differential Equations26 (1) (2006) 1-28. Zbl1151.35006MR2214879
17. [17] Kurzke M., A nonlocal singular perturbation problem with periodic well potential, ESAIM Control Optim. Calc. Var.12 (2006) 52-63. Zbl1107.49016MR2192068
18. [18] Lin F.H., Some dynamical properties of Ginzburg–Landau vortices, Comm. Pure Appl. Math.49 (4) (1996) 323-359. Zbl0853.35058
19. [19] Lin F.H., A remark on the previous paper: “Some dynamical properties of Ginzburg–Landau vortices”, Comm. Pure Appl. Math.49 (4) (1996) 361-364. Zbl0853.35059
20. [20] Moser R., Boundary vortices for thin ferromagnetic films, Arch. Rational Mech. Anal.174 (2004) 267-300. Zbl1099.82025MR2098108
21. [21] Moser R., Ginzburg–Landau vortices for thin ferromagnetic films, Applied Mathematics Research eXpress 2003 (1) (2003) 1-32. Zbl1057.35070
22. [22] Moser R., Moving boundary vortices for a thin-film limit in micromagnetics, Comm. Pure Appl. Math.58 (2005) 701-721. Zbl1080.35155MR2141896
23. [23] Sandier E., Serfaty S., Gamma-convergence of gradient flows with applications to Ginzburg–Landau, Comm. Pure Appl. Math.57 (12) (2004) 1627-1672. Zbl1065.49011
24. [24] Sandier E., Serfaty S., A product-estimate for Ginzburg–Landau and corollaries, J. Funct. Anal.211 (1) (2004) 219-244. Zbl1063.35144
25. [25] Serfaty S., Local minimizers for the Ginzburg–Landau energy near critical magnetic field. I, Commun. Contemp. Math.1 (2) (1999) 213-254. Zbl0944.49007
26. [26] Serfaty S., Local minimizers for the Ginzburg–Landau energy near critical magnetic field. II, Commun. Contemp. Math.1 (3) (1999) 295-333. Zbl0964.49005
27. [27] Toland J.F., The Peierls–Nabarro and Benjamin–Ono equations, J. Funct. Anal.145 (1) (1997) 136-150. Zbl0876.35106