The relaxed energy for S 2 -valued maps and measurable weights

Vincent Millot

Annales de l'I.H.P. Analyse non linéaire (2006)

  • Volume: 23, Issue: 2, page 135-157
  • ISSN: 0294-1449

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Millot, Vincent. "The relaxed energy for ${S}^{2}$-valued maps and measurable weights." Annales de l'I.H.P. Analyse non linéaire 23.2 (2006): 135-157. <http://eudml.org/doc/78687>.

@article{Millot2006,
author = {Millot, Vincent},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {dipole removing technique; lower bound of energy},
language = {eng},
number = {2},
pages = {135-157},
publisher = {Elsevier},
title = {The relaxed energy for $\{S\}^\{2\}$-valued maps and measurable weights},
url = {http://eudml.org/doc/78687},
volume = {23},
year = {2006},
}

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
PB - Elsevier
VL - 23
IS - 2
SP - 135
EP - 157
LA - eng
KW - dipole removing technique; lower bound of energy
UR - http://eudml.org/doc/78687
ER -

References

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  1. [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 Linéaire7 (1990) 269-286. Zbl0708.58004MR1067776
  2. [2] Bethuel F., The approximation problem for Sobolev maps between two manifolds, Acta Math.167 (1991) 153-206. Zbl0756.46017MR1120602
  3. [3] Bethuel F., Zheng X., Density of smooth functions between two manifolds in Sobolev spaces, J. Funct. Anal.80 (1988) 60-75. Zbl0657.46027MR960223
  4. [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. Zbl0793.58011MR1205144
  5. [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. Zbl1051.49030MR2075883
  6. [6] H. Brezis, Liquid crystals and energy estimates for S 2 -valued maps, in [11]. 
  7. [7] Brezis H., Coron J.M., Large solutions for harmonic maps in two dimensions, Comm. Math. Phys.92 (1983) 203-215. Zbl0532.58006MR728866
  8. [8] Brezis H., Coron J.M., Lieb E., Harmonics maps with defects, Comm. Math. Phys.107 (1986) 649-705. Zbl0608.58016MR868739
  9. [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. Zbl1078.46020MR2127792
  10. [10] Dal Maso G., Introduction to Γ-Convergence, Progr. Nonlinear Differential Equations Appl., vol. 8, Birkhäuser, 1993. Zbl0816.49001
  11. [11] Ericksen J., Kinderlehrer D. (Eds.), Theory and Applications of Liquid Crystals, IMA Ser., vol. 5, Springer, 1987. Zbl0713.76006MR900827
  12. [12] Giaquinta M., Modica G., Souček J., Cartesian Currents in the Calculus of Variations, Springer, 1998. Zbl0914.49001MR1645086
  13. [13] V. Millot, Energy with weight for S 2 -valued maps with prescribed singularities, Calculus of Variations and PDEs, in press. Zbl1115.49013

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