The Dirichlet-problem for harmonic maps from the disk into a lorentzian warped product

Carlo Greco

Annales de l'I.H.P. Analyse non linéaire (1993)

  • Volume: 10, Issue: 2, page 239-252
  • ISSN: 0294-1449

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Greco, Carlo. "The Dirichlet-problem for harmonic maps from the disk into a lorentzian warped product." Annales de l'I.H.P. Analyse non linéaire 10.2 (1993): 239-252. <http://eudml.org/doc/78302>.

@article{Greco1993,
author = {Greco, Carlo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Dirichlet problem; critical point theory; harmonic maps; Riemannian manifold; Lorentzian manifold},
language = {eng},
number = {2},
pages = {239-252},
publisher = {Gauthier-Villars},
title = {The Dirichlet-problem for harmonic maps from the disk into a lorentzian warped product},
url = {http://eudml.org/doc/78302},
volume = {10},
year = {1993},
}

TY - JOUR
AU - Greco, Carlo
TI - The Dirichlet-problem for harmonic maps from the disk into a lorentzian warped product
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1993
PB - Gauthier-Villars
VL - 10
IS - 2
SP - 239
EP - 252
LA - eng
KW - Dirichlet problem; critical point theory; harmonic maps; Riemannian manifold; Lorentzian manifold
UR - http://eudml.org/doc/78302
ER -

References

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  1. [1] V. Benci and J.M. Coron, The Dirichlet problem for harmonic maps from the disk into the euclidean n-sphere, Ann. Inst. H. Poincaré, Vol. 2, 1985, pp. 119-141. Zbl0597.35022MR794003
  2. [2] V. Benci, D. Fortunato and F. Giannoni, On the existence of multiple geodesics in static space-times, Ann. Inst. H. Poincaré, Vol. 8, 1991, pp. 79-102. Zbl0716.53057MR1094653
  3. [3] H. Brezis and J.M. Coron, Large solutions for harmonic maps in two dimension, Comm. Math. Phys., Vol. 92, 1983, pp. 203-215. Zbl0532.58006MR728866
  4. [4] J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc., Vol. 10, 1978, pp. 1-68. Zbl0401.58003MR495450
  5. [5] J. Eells and J.H. Sampson, Harmonic maps of riemannian manifold, Amer. J. Math., Vol. 86, 1964, pp. 109-160. Zbl0122.40102MR164306
  6. [6] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer, New York, 1977. Zbl0361.35003MR473443
  7. [7] C. Greco, Multiple periodic trajectories on stationary space-times, Ann. Mat. Pura e Appl., Vol. 162, 1992, pp. 337-348. Zbl0777.53066MR1199661
  8. [8] C.H. Gu, On the Cauchy problem for harmonic maps defined on two-dimensional Minkowski space, Comm. Pure Appl. Math., Vol. 33, 1980, pp. 727-737. Zbl0475.58005MR596432
  9. [9] O.A. Ladyzenskaja and N.N. Ural'ceva, Équations aux dérivées partielles de type elliptique, Dunod, Paris, 1968. Zbl0164.13001MR239273
  10. [10] Ma Li, On equivariant harmonic maps into a Lorentz manifold, 1990, preprint. Zbl0716.58008MR1075666
  11. [11] C.B. Morrey, Multiple integrals in the calculus of variations, Springer, New York, 1966. Zbl0142.38701MR202511
  12. [12] B. O'Neill, Semi-riemannian geometry, With applications to relativity, Academic Press, London, 1983. Zbl0531.53051MR719023
  13. [13] J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. Math., Vol. 113, 1981, pp. 1-24. Zbl0462.58014MR604040
  14. [14] R. Schoen and K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geometry, Vol. 18, 1983, pp. 253-268. Zbl0547.58020MR710054
  15. [15] J. Shatah, Weak solutions and development of singularities of the SU (2) σ-model, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 459-469. Zbl0686.35081MR933231

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