Acta Mathematica

, Volume 167, Issue 1, pp 153–206 | Cite as

The approximation problem for Sobolev maps between two manifolds

  • Fabrice Bethuel


Manifold Approximation Problem 
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  1. [Be1]Bethuel, F., A characterization of maps inH 1(B 3,S 2) which can be approximated by smooth maps. To appear.Google Scholar
  2. [BBC]Bethuel, F., Brezis, H. & Coron, J. M., Relaxed energies for harmonic maps. To appear.Google Scholar
  3. [BZ]Bethuel, F. &Zheng, X., Density of smooth functions between two manifolds in Sobolev spaces.J. Funct. Anal. 80 (1988), 60–75.CrossRefMathSciNetGoogle Scholar
  4. [BCL]Brezis, H., Coron, J. M. &Lieb, E., Harmonic maps with defects.Comm. Math. Phys., 107 (1986), 649–705.CrossRefMathSciNetGoogle Scholar
  5. [CG]Coron, J. M. & Gulliver, R., Minimizingp-harmonic maps into spheres. To appear.Google Scholar
  6. [EL]Eells, J. &Lemaire, L., A report on harmonic maps.Bull. London Math. Soc., 10 (1978), 1–68.MathSciNetGoogle Scholar
  7. [E]Escobedo, M. To appear.Google Scholar
  8. [F]Fuchs, M.,p-harmonic Hindernisprobleme. Habilitationsschrift, Düsseldorf, 1987.Google Scholar
  9. [HL]Hardt, R. &Lin, F. H., Mappings minimizing theL p norm of the gradient.Comm. Pure Appl. Math., 40 (1987), 556–588.MathSciNetGoogle Scholar
  10. [H]Helein, F., Approximations of Sobolev maps between an open set and an Euclidean sphere, boundary data, and singularities. To appear.Google Scholar
  11. [KW]Karcher, M. &Wood, J. C., Non existence results and growth properties for harmonic maps and forms.J. Reine Angew. Math., 353 (1984), 165–180.MathSciNetGoogle Scholar
  12. [L]Luckhaus, S., Partial Hölder continuity of minima of certain energies among maps into a Riemannian manifold. To appear inIndiana Univ. Math. J. Google Scholar
  13. [SU1]Schoen, R. &Uhlenbeck, K., A regularity theory for harmonic maps.J. Differential Geom., 17 (1982), 307–335.MathSciNetGoogle Scholar
  14. [SU2]—, Boundary regularity and the Dirichlet problem for harmonic maps.J. Differential Geom., 18 (1983), 253–268.MathSciNetGoogle Scholar
  15. [SU3]Schoen, R. & Uhlenbeck, K., Approximation theorems for Sobolev mappings. To appear.Google Scholar
  16. [W1]White, B., Infima of energy functionals in homotopy classes.J. Differential Geom., 23 (1986), 127–142.zbMATHMathSciNetGoogle Scholar
  17. [W2]—, Homotopy classes in Sobolev spaces and the existence of energy minimizing maps.Acta Math., 160 (1988), 1–17.zbMATHMathSciNetGoogle Scholar
  18. [Wo]Wood, J. C., Non existence of solution to certain Dirichlet problems for harmonic maps. Preprint Leeds University (1981).Google Scholar

Copyright information

© Almqvist & Wiksell 1991

Authors and Affiliations

  • Fabrice Bethuel
    • 1
  1. 1.ENPC, CERMANoisy-Le-GrandFrance

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