no. 2
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 
@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},
     pages = {135--157},
     year = {2006},
     publisher = {Elsevier},
     volume = {23},
     number = {2},
     doi = {10.1016/j.anihpc.2005.02.003},
     mrnumber = {2201149},
     zbl = {05024482},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2005.02.003/}
}
TY  - JOUR
AU  - Millot, Vincent
TI  - The relaxed energy for ${S}^{2}$-valued maps and measurable weights
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2006
SP  - 135
EP  - 157
VL  - 23
IS  - 2
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2005.02.003/
DO  - 10.1016/j.anihpc.2005.02.003
LA  - en
ID  - AIHPC_2006__23_2_135_0
ER  - 
%0 Journal Article
%A Millot, Vincent
%T The relaxed energy for ${S}^{2}$-valued maps and measurable weights
%J Annales de l'I.H.P. Analyse non linéaire
%D 2006
%P 135-157
%V 23
%N 2
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2005.02.003/
%R 10.1016/j.anihpc.2005.02.003
%G en
%F 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

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

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

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

[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. | Zbl | MR

[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. | Zbl | MR | Numdam

[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. | Zbl | MR

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

[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. | Zbl | MR

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

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

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

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

Cité par Sources :