The Dirichlet problem for harmonic maps from the disk into the euclidean n-sphere
Annales de l'I.H.P. Analyse non linéaire (1985)
- Volume: 2, Issue: 2, page 119-141
- ISSN: 0294-1449
Access Full Article
topHow to cite
topBenci, V., and Coron, J. M.. "The Dirichlet problem for harmonic maps from the disk into the euclidean n-sphere." Annales de l'I.H.P. Analyse non linéaire 2.2 (1985): 119-141. <http://eudml.org/doc/78091>.
@article{Benci1985,
author = {Benci, V., Coron, J. M.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {2},
pages = {119-141},
publisher = {Gauthier-Villars},
title = {The Dirichlet problem for harmonic maps from the disk into the euclidean n-sphere},
url = {http://eudml.org/doc/78091},
volume = {2},
year = {1985},
}
TY - JOUR
AU - Benci, V.
AU - Coron, J. M.
TI - The Dirichlet problem for harmonic maps from the disk into the euclidean n-sphere
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1985
PB - Gauthier-Villars
VL - 2
IS - 2
SP - 119
EP - 141
LA - eng
UR - http://eudml.org/doc/78091
ER -
References
top- [A] Th. Aubin, Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire. J. Math. Pures et Appl., t. 55, 1976, p. 269-296. Zbl0336.53033MR431287
- [BC1] H. Brezis, J.M. Coron, Multiple solutions of H-systems and Rellich's conjecture. Comm. Pure Appl. Math. t. XXXVII, 1984, p. 149-187. Zbl0537.49022MR733715
- [BC2] H. Brezis, J.M. Coron, Large solutions for harmonic maps in two dimensions, Comm. Math. Phys. t. 92, 1983, p. 203-215. Zbl0532.58006MR728866
- [BN] H. Brezis, L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. t. XXXVI, 1983, p. 437- 477. Zbl0541.35029MR709644
- [C] E. Calabi, Minimal immersions of surfaces in Euclidean spheres. J. Diff. Geometry, t. 1, 1967, p. 111-125. Zbl0171.20504MR233294
- [GOR] R.D. Gulliver, R. Osserman, H.L. Royden, A theory of branched immersions of surfaces. Amer. J. Math., t. 95, 1973, p. 750-812. Zbl0295.53002MR362153
- [GT] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl0361.35003MR473443
- [HW] S. Hildebrandt, K.O. Widman, Some regularity results for quasilinear elliptic systems of second order. Math. Z., t. 142, 1975, p. 67-86. Zbl0317.35040MR377273
- [J] J. Jost, The Dirichlet problem for harmonic maps from a surface with boundary onto a 2-sphere with nonconstant boundary values. J. Diff. Geometry (to appear). Zbl0551.58012MR755231
- [LU1] O.A. Ladyzenskaya, N.N. Ural'ceva, Linear and Quasilinear Elliptic Equations. New York and London: Academic Press, 1968. Zbl0164.13002MR244627
- [LU2] O.A. Ladyzenskaya, N.N. Ural'ceva, Linear and quasilinear elliptic equations, second Russian edition, Moscow, Nauka, 1973.
- [LM] L. Lemaire, Applications harmoniques de surfaces riemanniennes. J. Diff. Geometry, t. 13, 1978, p. 51-78. Zbl0388.58003MR520601
- [LB] E. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Annals of Math. (to appear). Zbl0527.42011MR717827
- [LN] P.L. Lions, The concentration compactness principle in the calculus of variations the limit case. Riv. Iberoamericana (to appear) and Comptes Rendus Acad. Sc. Paris, t. 296, série I, 1983, p. 645-648. Zbl0522.49008MR705681
- [M1] C.B. Morrey, On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc., t. 431938, p. 126-166. Zbl0018.40501MR1501936
- [M2] C.B. Morrey, Multiple Integrals in the Calculus of Variations. Springer-Verlag, Berlin-Heidelberg-New York, 1966. Zbl0142.38701MR202511
- [N] L. Nirenberg, On nonlinear elliptic partial differential equations and Hölder continuity. Comm. Pure App. Math., t. 6, 1953, p. 103-156. Zbl0050.09801MR64986
- [SU1] J. Sacks, K. Uhlenbeck, The existence of minimal immersions of 2-spheres. Annals of Math., t. 113, 1981, p. 1-24. Zbl0462.58014MR604040
- [SU2] R. Schoen, K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps. J. Diff. Geometry, t. 18, 1983, p. 253-268. Zbl0547.58020MR710054
- [St] M. Struwe, Nonuniqueness in the Plateau problem for surfaces of constant mean curvature (to appear). Zbl0603.49027MR823116
- [T] C. Taubes, The existence of a non-minimal solution to the SU(2) Yang-Mills-Higgs equations on R3 (to appear). Zbl0514.58016
- [W1] H. Wente, The differential equation Δx = 2Hxu ^ xv with vanishing boundary values. Proc. A. M. S., t. 50, 1975, p. 131-137. Zbl0313.35030MR374673
- [W2] H. Wente, The Dirichlet problem with a volume constraint. Manuscripta Math., t. 11, 1974, p. 141-157. Zbl0268.35031MR328752
- [Wi] M. Wiegner, A-priori Schranken für Lösungen gewisser elliptischer Systeme. Math. Z., t. 147, 1976, p. 21-28. Zbl0316.35039MR407430
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.