Heat flow and boundary value problem for harmonic maps

Chang Kung-Ching

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: 6, Issue: 5, page 363-395
  • ISSN: 0294-1449

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Kung-Ching, Chang. "Heat flow and boundary value problem for harmonic maps." Annales de l'I.H.P. Analyse non linéaire 6.5 (1989): 363-395. <http://eudml.org/doc/78184>.

@article{Kung1989,
author = {Kung-Ching, Chang},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {heat equation; minimax principle; parabolic system; harmonic map; Ljusternik-Schnirelmann},
language = {eng},
number = {5},
pages = {363-395},
publisher = {Gauthier-Villars},
title = {Heat flow and boundary value problem for harmonic maps},
url = {http://eudml.org/doc/78184},
volume = {6},
year = {1989},
}

TY - JOUR
AU - Kung-Ching, Chang
TI - Heat flow and boundary value problem for harmonic maps
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - 6
IS - 5
SP - 363
EP - 395
LA - eng
KW - heat equation; minimax principle; parabolic system; harmonic map; Ljusternik-Schnirelmann
UR - http://eudml.org/doc/78184
ER -

References

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  2. [BrC1] H. Brezis and J.M. Coron, Large Solutions for Harmonic Maps in Two Dimensions, Comm. Math. Phys., T. 92, 1983, pp. 203-215. Zbl0532.58006MR728866
  3. [C1] K.C. Chang, Infinite Dimensional Morse Theory and its Applications, Univ. de Montréal, 1985. Zbl0609.58001MR837186
  4. [EL1] J. Eells and L. Lemaire, A Report on Harmonic Maps, Bull. London Math. Soc., Vol. 16, 1978, pp. 1-68. Zbl0401.58003MR495450
  5. [ES1] J. Eells and J.H. Sampson, Harmonic Mappings of Riemannian Manifolds, A.J.M., vol. 86, 1964, pp. 109-160. Zbl0122.40102MR164306
  6. [EW1] J. Eells and J.C. Wood, Restrictions on Harmonic Maps of Surfaces, Topology, Vol. 15, 1976, pp. 263-266. Zbl0328.58008MR420708
  7. [F1] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964. Zbl0144.34903MR181836
  8. [H1] R. Hamilton, Harmonic Maps of Manifolds with Boundary, L.N.M. No. 471, Springer, Berlin-Heidelberg-New York, 1975. Zbl0308.35003MR482822
  9. [J1] J. Jost, Ein Existenzbeweis für harmonische Abbildungen, dis ein Dirichlet-problem lösen, mittels der Methode der Wäumeflusses, Manusc. Math., Vol. 38, 1982, pp. 129-130. Zbl0486.58011
  10. [J2] J. Jost, The Dirichlet problem for harmonic maps from a surface with boundary onto a 2-sphere with nonconstant boundary values, J. Diff. Geometry, Vol. 19, 1984, pp. 393-401. Zbl0551.58012MR755231
  11. [LSU1] O.A. Ladyszenskaya, V.A. Solonnikov and N.N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, A.M.S. Transl. Math. Monogr.23, Providence, 1968. 
  12. [L1] L. Lemaire, Boundary Value Problems for Harmonic and Minimal Maps of Surfaces Into Manifolds, Ann. Scuola Norm. Sup. Pisa, (4), 9, 1982, pp. 91-103. Zbl0532.58004MR664104
  13. [N1] S.M. Nikol'ski, Approximation of Functions of Several Variables and Imbedding Theorems, Springer-Verlag, 1975. Zbl0307.46024MR374877
  14. [SU1] J. Sacks and K. Uhlenbeck, The Existence of Minimal Immersions of Two Spheres, Ann. Math., Vol. 113, 1981, pp. 1-24. Zbl0462.58014MR604040
  15. [St1] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton, 1970. Zbl0207.13501MR290095
  16. [S1] M. Struwe, On the Evolution of Harmonic Mappings, Commet. Math. Helvetici, Vol. 60, 1985, pp. 558-581. Zbl0595.58013MR826871
  17. [S2] M. Struwe, The Evolution of Harmonic Maps (Part I) Heat-Flow Methods for Harmonic Maps of Surfaces and Applications to Free Boundary Problems, I.C.T.P., 1988. MR965544
  18. [S3] M. Struwe, The Evolution of Harmonic Maps (Part II). On the Evolution of Harmonic Maps in Higher Dimensions, Jour. Diff. Geometry (to appear). Zbl0631.58004MR1159304
  19. [U1] K. Uhlenbeck, Morse Theory by Perturbation Methods with Applications to Harmonic Maps, T.A.M.S., 1981. Zbl0509.58012MR626490
  20. [VW1] W. Von Wahl, Verhalten der Lösungen parabolisher Gleischungen für t → ∞ mit Lösbarkeit in Grossen, Nachr. Akad. Wiss. Göttingen, 51981. MR656525
  21. [W1] R.H. Wang, A Fourier Method on the Lp Theory of Parabolic and Elliptic Boundary Value Problems, Scientia Sinica, 1965. Zbl0158.11801

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