The gradient flow motion of boundary vortices
Kurzke, Matthias
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007), p. 91-112 / Harvested from Numdam
@article{AIHPC_2007__24_1_91_0,
     author = {Kurzke, Matthias},
     title = {The gradient flow motion of boundary vortices},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {24},
     year = {2007},
     pages = {91-112},
     doi = {10.1016/j.anihpc.2005.12.002},
     mrnumber = {2286560},
     zbl = {1114.35022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_1_91_0}
}
Kurzke, Matthias. The gradient flow motion of boundary vortices. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 91-112. doi : 10.1016/j.anihpc.2005.12.002. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_1_91_0/

[1] Alberti G., Baldo S., Orlandi G., Variational convergence for functionals of Ginzburg-Landau type, Indiana Univ. Math. J. 54 (2005) 1411-1472. | Zbl 1160.35013 | Zbl pre02246719

[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. | MR 1289307 | Zbl 0845.49008

[3] Alberti G., Bouchitté G., Seppecher P., Phase transition with the line-tension effect, Arch. Rational Mech. Anal. 144 (1) (1998) 1-46. | MR 1657316 | Zbl 0915.76093

[4] Almeida L., Bethuel F., Topological methods for the Ginzburg-Landau equations, J. Math. Pures Appl. (9) 77 (1) (1998) 1-49. | Zbl 0904.35023

[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. | Zbl 0802.35142

[6] X. Cabré, N. Cónsul, Minimizers for boundary reactions: renormalized energy, location of singularities, and applications, in preparation.

[7] Cabré X., Solà-Morales J., Layer solutions in a half-space for boundary reactions, Comm. Pure Appl. Math. 58 (12) (2005) 1678-1732. | MR 2177165 | Zbl 1102.35034

[8] Carbou G., Thin layers in micromagnetism, Math. Models Methods Appl. Sci. 11 (9) (2001) 1529-1546. | MR 1872680 | Zbl 1012.82031

[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. | MR 1916988 | Zbl 1027.82042

[10] Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. | MR 1158660 | Zbl 0804.28001

[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. | Zbl pre05051266

[12] Gioia G., James R.D., Micromagnetics of very thin films, Proc. Roy. Soc. London Ser. A 453 (1997) 213-223.

[13] Jerrard R.L., Soner H.M., Dynamics of Ginzburg-Landau vortices, Arch. Rational Mech. Anal. 142 (2) (1998) 99-125. | Zbl 0923.35167

[14] Kohn R.V., Slastikov V.V., Another thin-film limit of micromagnetics, Arch. Rational Mech. Anal. 178 (2) (2005) 227-245. | MR 2186425 | Zbl 1074.78012

[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. | MR 2124197 | Zbl pre05206141

[16] Kurzke M., Boundary vortices in thin magnetic films, Calc. Var. Partial Differential Equations 26 (1) (2006) 1-28. | MR 2214879 | Zbl pre05032406

[17] Kurzke M., A nonlocal singular perturbation problem with periodic well potential, ESAIM Control Optim. Calc. Var. 12 (2006) 52-63. | Numdam | MR 2192068 | Zbl 1107.49016

[18] Lin F.H., Some dynamical properties of Ginzburg-Landau vortices, Comm. Pure Appl. Math. 49 (4) (1996) 323-359. | Zbl 0853.35058

[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. | Zbl 0853.35059

[20] Moser R., Boundary vortices for thin ferromagnetic films, Arch. Rational Mech. Anal. 174 (2004) 267-300. | MR 2098108 | Zbl 1099.82025

[21] Moser R., Ginzburg-Landau vortices for thin ferromagnetic films, Applied Mathematics Research eXpress 2003 (1) (2003) 1-32. | Zbl 1057.35070

[22] Moser R., Moving boundary vortices for a thin-film limit in micromagnetics, Comm. Pure Appl. Math. 58 (2005) 701-721. | MR 2141896 | Zbl 1080.35155

[23] Sandier E., Serfaty S., Gamma-convergence of gradient flows with applications to Ginzburg-Landau, Comm. Pure Appl. Math. 57 (12) (2004) 1627-1672. | Zbl 1065.49011

[24] Sandier E., Serfaty S., A product-estimate for Ginzburg-Landau and corollaries, J. Funct. Anal. 211 (1) (2004) 219-244. | Zbl 1063.35144

[25] Serfaty S., Local minimizers for the Ginzburg-Landau energy near critical magnetic field. I, Commun. Contemp. Math. 1 (2) (1999) 213-254. | Zbl 0944.49007

[26] Serfaty S., Local minimizers for the Ginzburg-Landau energy near critical magnetic field. II, Commun. Contemp. Math. 1 (3) (1999) 295-333. | Zbl 0964.49005

[27] Toland J.F., The Peierls-Nabarro and Benjamin-Ono equations, J. Funct. Anal. 145 (1) (1997) 136-150. | Zbl 0876.35106