A characterization of maps in H 1 ( B 3 , S 2 ) which can be approximated by smooth maps

F. Bethuel

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 4, page 269-286
  • ISSN: 0294-1449

How to cite


Bethuel, F.. "A characterization of maps in $H^1 (B^3, S^2)$ which can be approximated by smooth maps." Annales de l'I.H.P. Analyse non linéaire 7.4 (1990): 269-286. <http://eudml.org/doc/78224>.

author = {Bethuel, F.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {density of smooth maps; Sobolev space},
language = {eng},
number = {4},
pages = {269-286},
publisher = {Gauthier-Villars},
title = {A characterization of maps in $H^1 (B^3, S^2)$ which can be approximated by smooth maps},
url = {http://eudml.org/doc/78224},
volume = {7},
year = {1990},

AU - Bethuel, F.
TI - A characterization of maps in $H^1 (B^3, S^2)$ which can be approximated by smooth maps
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 4
SP - 269
EP - 286
LA - eng
KW - density of smooth maps; Sobolev space
UR - http://eudml.org/doc/78224
ER -


  1. [B] H. Brezis, private communication. 
  2. [BCL] H. Brezis, J.M. Coron and E.H. Lieb, Harmonic maps with defects.Comm. Math. Phys., t. 107, 1986, p. 649-705. Zbl0608.58016MR868739
  3. [Bel] F. Bethuel, The approximation problem for Sobolev maps between two manifolds, to appear. Zbl0756.46017MR1120602
  4. [BZ] F. Bethuel and X. Zheng, Density of smooth functions between two manifolds in Sobolev spaces. J. Func. Anal., t. 80, 1988, p. 60-75. Zbl0657.46027MR960223
  5. [CG] J.M. Coron and R. Gulliver, Minimizing p-harmonic maps into spheres, preprint. Zbl0677.58021MR1018054
  6. [H] F. Helein, Approximations of Sobolev maps between an open set and an euclidean sphere, boundary data, and singularities, preprint. Zbl0659.35002MR1010196
  7. [SU] R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps. J. Diff. Geom., t. 17, 1982, p. 307-335. Zbl0521.58021MR664498
  8. [W] B. White, Infima of energy functionals in homotopy classes. J. Diff. Geom, t. 23, 1986, p. 127-142. Zbl0588.58017MR845702

Citations in EuDML Documents

  1. Robert Hardt, Tristan Rivière, Ensembles singuliers topologiques dans les espaces fonctionnels entre variétés
  2. Rejeb Hadiji, Feng Zhou, A problem of minimization with relaxed energy
  3. Vincent Millot, The relaxed energy for S 2 -valued maps and measurable weights
  4. Fang Hua Lin, Rectifiability of defect measures, fundamental groups and density of Sobolev mappings
  5. Thiemo Kessel, Tristan Rivière, Singular Bundles with Bounded L 2 -Curvatures
  6. Robert Hardt, Tristan Rivière, Connecting topological Hopf singularities
  7. Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen, Density of smooth maps for fractional Sobolev spaces W s , p into simply connected manifolds when s 1
  8. Jean Bourgain, Haim Brezis, Petru Mironescu, H1/2 maps with values into the circle : minimal connections, lifting, and the Ginzburg–Landau equation
  9. Guido De Philippis, Weak notions of jacobian determinant and relaxation
  10. Guido De Philippis, Weak notions of Jacobian determinant and relaxation

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