Minimizers of the Lawrence-Doniach energy in the small-coupling limit : finite width samples in a parallel field
Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 3, pp. 281-312.
@article{AIHPC_2002__19_3_281_0,
     author = {Alama, S. and Berlinsky, A. J. and Bronsard, L.},
     title = {Minimizers of the {Lawrence-Doniach} energy in the small-coupling limit : finite width samples in a parallel field},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {281--312},
     publisher = {Elsevier},
     volume = {19},
     number = {3},
     year = {2002},
     zbl = {1011.82032},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2002__19_3_281_0/}
}
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Alama, S.; Berlinsky, A. J.; Bronsard, L. Minimizers of the Lawrence-Doniach energy in the small-coupling limit : finite width samples in a parallel field. Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 3, pp. 281-312. http://www.numdam.org/item/AIHPC_2002__19_3_281_0/

[1] Alama S., Berlinsky A.J., Bronsard L., Periodic vortex lattices for the Lawrence-Doniach model of layered superconductors in a parallel field, preprint, 2000, available on the preprint archive http://xxx.lanl.gov. | MR

[2] Ambrosetti A., Badiale M., Homoclinics: Poincaré-Melnikov type results via a variational approach, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 233-252. | Numdam | MR | Zbl

[3] Ambrosetti A., Coti-Zelati V., Ekeland I., Symmetry breaking in Hamiltonian systems, J. Differential Equations 67 (1987) 165-184. | MR | Zbl

[4] Bahri A., Li Y., Rey O., On a variational problem with lack of compactness: the topological effect of the critical points at infinity, Calc. Var. Partial Differential Equations 3 (1995) 67-93. | MR | Zbl

[5] Bethuel F., Brezis H., Hélein F., Ginzburg-Landau Vortices, Birkhauser, Boston, 1994. | MR | Zbl

[6] Bethuel F., Riviére T., Vortices for a variational problem related to superconductivity, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995) 243-303. | Numdam | MR | Zbl

[7] Bulaevskii L., Magnetic properties of layered superconductors with weak interaction between the layers, Sov. Phys. JETP 37 (1973) 1133-1136.

[8] Bulaevskii L., Clem J., Vortex lattice of highly anisotropic layered superconductors in strong, parallel magnetic fields, Phys. Rev. B44 (1991) 10234-10238.

[9] Chapman S., Du Q., Gunzburger M., On the Lawrence-Doniach and anisotropic Ginzburg-Landau models for layered superconductors, SIAM J. Appl. Math. 55 (1995) 156-174. | MR | Zbl

[10] Clem J., Coffey M., Viscous flux motion in a Josephson-coupled layer model of high-Tc superconductors, Phys. Rev. B42 (1990) 6209-6216.

[11] Del Pino M., Felmer P., Local minimizers for the Ginzburg-Landau energy, Math. Z. 225 (1997) 671-684. | MR | Zbl

[12] Giorgi T., Phillips D., The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model, SIAM J. Math. Anal. 30 (1999) 341-359. | MR | Zbl

[13] Grisvard P., Elliptic Problems in Nonsmooth Domains, Pitman Advanced Publishing Program, Boston, 1985. | MR | Zbl

[14] Gui C., Multipeak solutions for a semilinear Neumann problem, Duke Math. J. 84 (1996) 739-769. | MR | Zbl

[15] Iye Y., How anisotropic are the cuprate high Tc superconductors?, Comments Cond. Mat. Phys. 16 (1992) 89-111.

[16] Kes P., Aarts J., Vinokur V., Van Der Beek C., Dissipation in highly anisotropic superconductors, Phys. Rev. Lett. 64 (1990) 1063-1066.

[17] S. Kuplevakhsky, Microscopic theory of weakly couple superconducting multilayers in an external magnetic field, preprint cond-mat/9812277.

[18] Lawrence W., Doniach S., Proceedings of the Twelfth International Conference on Low Temperature Physics, E. Kanda (Ed.), Academic Press of Japan, Kyoto, 1971, p. 361.

[19] Li Y., Nirenberg L., The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math. 51 (1998) 1445-1490. | MR | Zbl

[20] Lieb E., Loss M., Analysis Graduate Studies in Mathematics, 14, American Mathematical Society, Providence, RI, 1997. | MR | Zbl

[21] Rubinstein J., Schatzman M., Asymptotics for thin superconducting rings, J. Math. Pures Appl., série 9 77 (1998) 801-820. | MR | Zbl

[22] Rey O., Blow-up points of solutions to elliptic equations with limiting nonlinearity, Differential Integral Equations 4 (1991) 1155-1167. | MR | Zbl

[23] Theorodakis S., Theory of vortices in weakly-Josephson-coupled layered superconductors, Phys. Rev. B42 (1990) 10172-10177.

[24] Tinkham M., Introduction to Superconductivity, Mc Graw-Hill, New York, 1996.

[25] Wei J., On the interior spike solutions for some singular perturbation problems, Proc. Roy. Soc. Edinburgh, Sect. A 128 (1998) 849-874. | MR | Zbl