Asymptotic Analysis, in a Thin Multidomain, of Minimizing Maps With Values in S 2
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 1, p. 59-80
@article{AIHPC_2009__26_1_59_0,
     author = {Gaudiello, Antonio and Hadiji, Rejeb},
     title = {Asymptotic Analysis, in a Thin Multidomain, of Minimizing Maps With Values in ${S}^{2}$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {26},
     number = {1},
     year = {2009},
     pages = {59-80},
     doi = {10.1016/j.anihpc.2007.06.002},
     zbl = {1156.78300},
     mrnumber = {2483813},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2009__26_1_59_0}
}
Gaudiello, Antonio; Hadiji, Rejeb. Asymptotic Analysis, in a Thin Multidomain, of Minimizing Maps With Values in ${S}^{2}$. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 1, pp. 59-80. doi : 10.1016/j.anihpc.2007.06.002. http://www.numdam.org/item/AIHPC_2009__26_1_59_0/

[1] Alicandro R., Corbo Esposito A., Leone C., Relaxation in BV of Integral Functionals Defined on Sobolev Functions With Values in the Unit Sphere, J. Convex Anal. 14 (1) (2007) 69-98. | MR 2310429 | Zbl 1138.49017

[2] Bethuel F., Brezis H., Hélein F., Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994. | MR 1269538 | Zbl 0802.35142

[3] Bethuel F., Zheng X., Density of Smooth Functions Between Two Manifolds in Sobolev Spaces, J. Funct. Anal. 80 (2) (1988) 60-75. | MR 960223 | Zbl 0657.46027

[4] Ciarlet P. G., Plates and Junctions in Elastic Multistructures: an Asymptotic Analysis, Research in Applied Mathematics, vol. 14, Masson, Springer-Verlag, Paris, Berlin, 1990. | MR 1071376 | Zbl 0706.73046

[5] Ciarlet P. G., Destuynder P., A Justification of the Two-Dimensional Linear Plate Model, J. Mécanique 18 (2) (1979) 315-344. | MR 533827 | Zbl 0415.73072

[6] Cioranescu D., Saint Jean Paulin J., Homogenization of Reticulated Structures, Applied Mathematical Sciences, vol. 139, Springer-Verlag, New York, 1999. | MR 1676922 | Zbl 0929.35002

[7] Courilleau P., Hadiji R., Dumont S., Regularity of Minimizing Maps With Values in S 2 and Some Numerical Simulations, Adv. Math. Sci. Appl. 10 (2) (2000) 711-733. | MR 1807449 | Zbl 0979.49029

[8] Damlamian A., Vogelius M., Homogenization Limits of the Equations of Elasticity in Thin Domains, SIAM J. Math. Anal. 18 (2) (1987) 435-451. | MR 876283 | Zbl 0614.73012

[9] De Giorgi E., Franzoni T., Su Un Tipo Di Convergenza Variazionale, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (8) (6) (1975) 842-850. | MR 448194 | Zbl 0339.49005

[10] Gaudiello A., Gustafsson B., Lefter C., Mossino J., Coupled and Uncoupled Limits for a N-Dimensional Multidomain Neumann Problem, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000) 985-990. | MR 1779691 | Zbl 0955.35028

[11] Gaudiello A., Gustafsson B., Lefter C., Mossino J., Asymptotic Analysis of a Class of Minimization Problems in a Thin Multidomain, Calc. Var. Partial Differential Equations 15 (2) (2002) 181-201. | MR 1930246 | Zbl 1003.49013

[12] Gaudiello A., Gustafsson B., Lefter C., Mossino J., Asymptotic Analysis for Monotone Quasilinear Problems in Thin Multidomains, Differential Integral Equations 15 (5) (2002) 623-640. | MR 1895899 | Zbl 1034.35020

[13] Gaudiello A., Monneau R., Mossino J., Murat F., Sili A., On the Junction of Elastic Plates and Beams, C. R. Acad. Sci. Paris Sér. I Math. 335 (8) (2002) 717-722. | MR 1941655 | Zbl 1032.74037

[14] Gaudiello A., Monneau R., Mossino J., Murat F., Sili A., Junction of Elastic Plates and Beams, ESAIM Control Optim. Calc. Var. 13 (3) (2007) 419-457. | Numdam | MR 2329170 | Zbl 1133.35322

[15] Gaudiello A., Sili A., Asymptotic Analysis of the Eigenvalues of a Laplacian Problem in a Thin Multidomain, Indiana Univ. Math. J. 56 (4) (2007) 1675-1710. | MR 2354696 | Zbl pre05203544

[16] Gaudiello A., Zappale E., Junction in a Thin Multidomain for a Fourth Order Problem, 16 (12) (2006) 1887-1918. | MR 2287334 | Zbl 1109.74032

[17] Guo B. H., Hong M. C., The Landau-Lifshitz Equation of the Ferromagnetic Spin Chain and Harmonic Maps, Calc. Var. Partial Differential Equations 1 (3) (1993) 311-334. | MR 1261548 | Zbl 0798.35139

[18] Hadiji R., Zhou F., Regularity of Ω u 2 +λ Ω |u-f| 2 and Some Gap Phenomenon, Potential Anal. 1 (1992) 385-400. | MR 1245894 | Zbl 0794.35036

[19] Hong M. C., The Landau-Lifshitz Equation With the External Field - a New Extension Or Harmonic Maps With Values in S 2 , Math. Z. 220 (2) (1995) 171-188. | MR 1355024 | Zbl 0843.35028

[20] Gruais I., Modélisation De La Jonction Entre Une Plaque Et Une Poutre En Élasticité Linéarisée, RAIRO Modél. Math. Anal. Numér. 27 (1) (1993) 77-105. | Numdam | MR 1204630 | Zbl 0767.73034

[21] Kozlov V. A., Ma'Zya V. G., Movchan A. B., Asymptotic Analysis of Fields in a Multi-Structure, Oxford Mathematical Monographs. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1999. | MR 1860617 | Zbl 0951.35004

[22] Landau L. D., Lifshitz E. M., On the Theory of the Dispersion of Magnetic Permeability in Ferromagnetic Bodies, Phys. Z. Sowjetunion 8 (1935) 153, Reproduced, in: Collected Papers of L.D. Landau, Pergamon Press, New York, 1965, pp. 101-114. | Zbl 0012.28501

[23] Le Dret H., Problèmes Variationnels Dans Le Multi-Domaines: Modélisation Des Jonctions Et Applications, Research in Applied Mathematics, vol. 19, Masson, Paris, 1991. | Zbl 0744.73027

[24] Smith K. T., Primer of Modern Analysis, Springer-Verlag, New York, 1983. | MR 710655 | Zbl 0517.26001

[25] Stanley H. E., Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, New York and Oxford, 1971.

[26] Struwe M., Une Estimation Asymptotique Pour Le Modèle De Ginzburg-Landau, C. R. Acad. Sci. Paris Sér. I Math. 317 (7) (1993) 677-680. | MR 1245097 | Zbl 0789.49005

[27] Trabucho L., Viano J. M., Mathematical Modelling of Rods, Handbook of Numerical Analysis, vol. 4, North-Holland, Amsterdam, 1996. | MR 1422507 | Zbl 0873.73041