Nonuniqueness for the heat flow of harmonic maps

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 7, Issue 4, 1990, Pages 335-344

  Coron, J M ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

58E20; 58G11; Harmonic maps; Heat flow; Uniqueness

Indexed keywords

58E20; 58G11; CAUCHY PROBLEMS; HARMONIC MAP; NONUNIQUENESS; UNIQUENESS; WEAK SOLUTION;

HEAT TRANSFER;

EID: 0001205332     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(16)30295-5     Document Type: Article

References (11)

1. Brezis, H., Coron, J.M., Lieb, E.H., Harmonic maps with defects. Comm. Math. Phys. t. 107 (1986), 649–705.
2. Chen, Y., Weak solutions to the evolution problem for harmonic maps into spheres, preprint. Math. Z. t. 201 (1989), 69–74.
3. Chen, Y., Struwe, M., Existence and partial regularity results for the heat flow for harmonic maps. Math. Z. t. 201 (1989), 83–103.
4. Cohen, R., Hardt, R., Kinderlehrer, D., Lin, S.Y., Luskin, M., Minimum energy configurations from liquid crystals: computational results, Theory and Appl. of liquid crystals. I. M. A. Vol. Math. Appl., vol. 5, 1987, Springer, 99–122.
5. Coron, J.M., Ghidaglia, J.M., Explosion en temps fini pour le flot des applications harmoniques. C. R. Acad. Sci. Paris t. 308 (1989), 339–344.
6. Eells, J., Sampson, J.H., Harmonic mappings of Riemannian manifolds. Am. J. Math. t. 86 (1964), 109–160.
7. Hardt, R., Kinderlehrer, D., Lin, F.H., Stable defects of minimizers of constrained variational principles. Ann. Inst. Henri Poincaré Analyse Non Linéaire t. 5 (1988), 297–322.
8. J. Keller, J. Rubinstein and P. Sternberg, Reaction diffusion processes and evolution to harmonic maps, preprint, 1988.
9. Price, P., A monotonicity formula for Yang-Mills fields. Manuscripta Math. t. 43 (1983), 131–166.
10. Struwe, M., On the evolution of harmonic maps in higher dimension. J. Diff. Geom. t. 28 (1988), 485–502.
11. Struwe, M., On the evolution of harmonic maps of Riemannian surfaces. Comm. Math. Helv. t. 60 (1985), 558–581.