The relaxed energy for ${S}^{2}$-valued maps and measurable weights
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 2, p. 135-157
@article{AIHPC_2006__23_2_135_0,
author = {Millot, Vincent},
title = {The relaxed energy for ${S}^{2}$-valued maps and measurable weights},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {23},
number = {2},
year = {2006},
pages = {135-157},
doi = {10.1016/j.anihpc.2005.02.003},
zbl = {05024482},
mrnumber = {2201149},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2006__23_2_135_0}
}

Millot, Vincent. The relaxed energy for ${S}^{2}$-valued maps and measurable weights. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 2, pp. 135-157. doi : 10.1016/j.anihpc.2005.02.003. http://www.numdam.org/item/AIHPC_2006__23_2_135_0/

[1] Bethuel F., A characterization of maps in ${H}^{1}\left({B}^{3},{S}^{2}\right)$ which can be approximated by smooth maps, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 269-286. | Numdam | MR 1067776 | Zbl 0708.58004

[2] Bethuel F., The approximation problem for Sobolev maps between two manifolds, Acta Math. 167 (1991) 153-206. | MR 1120602 | Zbl 0756.46017

[3] Bethuel F., Zheng X., Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal. 80 (1988) 60-75. | MR 960223 | Zbl 0657.46027

[4] Bethuel F., Brezis H., Coron J.M., Relaxed energies for harmonic maps, in: Berestycki H., Coron J.M., Ekeland I. (Eds.), Variational Problems, Birkhäuser, 1990, pp. 37-52. | MR 1205144 | Zbl 0793.58011

[5] J. Bourgain, H. Brezis, P. Mironescu, ${H}^{1/2}$-maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation, Publ. Math. Inst. Hautes Etudes Sci., in press. | Numdam | MR 2075883 | Zbl 1051.49030

[6] H. Brezis, Liquid crystals and energy estimates for ${S}^{2}$-valued maps, in [11].

[7] Brezis H., Coron J.M., Large solutions for harmonic maps in two dimensions, Comm. Math. Phys. 92 (1983) 203-215. | MR 728866 | Zbl 0532.58006

[8] Brezis H., Coron J.M., Lieb E., Harmonics maps with defects, Comm. Math. Phys. 107 (1986) 649-705. | MR 868739 | Zbl 0608.58016

[9] H. Brezis, P.M. Mironescu, A.C. Ponce, ${W}^{1,1}$-maps with values into ${S}^{1}$, in: S. Chanillo, P. Cordaro, N. Hanges, J. Hounie, A. Meziani (Eds.), Geometric Analysis of PDE Several Complex Variables, Contemp. Math., AMS, in press. | MR 2127792 | Zbl 1078.46020

[10] Dal Maso G., Introduction to Γ-Convergence, Progr. Nonlinear Differential Equations Appl., vol. 8, Birkhäuser, 1993. | Zbl 0816.49001

[11] Ericksen J., Kinderlehrer D. (Eds.), Theory and Applications of Liquid Crystals, IMA Ser., vol. 5, Springer, 1987. | MR 900827 | Zbl 0713.76006

[12] Giaquinta M., Modica G., Souček J., Cartesian Currents in the Calculus of Variations, Springer, 1998. | MR 1645086 | Zbl 0914.49001

[13] V. Millot, Energy with weight for ${S}^{2}$-valued maps with prescribed singularities, Calculus of Variations and PDEs, in press. | Zbl 02204799