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On Eells-Sampson’s existence theorem for harmonic maps via exponentially harmonic maps
Published online by Cambridge University Press: 11 January 2016
Abstract
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In this note, we introduce an approximation of harmonic maps via a sequence of exponentially harmonic maps. We then reestablish the existence theorem of harmonic maps due to Eells and Sampson.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2011
References
[1]
Duc, D. M., Variational problems of certain functionals, Internat. J. Math.
6 (1995), 503–535.Google Scholar
[2]
Duc, D. M. and Eells, J., Regularity of exponentially harmonic functions, Internat. J. Math.
2 (1991), 395–408.Google Scholar
[3]
Eells, J. and Lemaire, L., “Some properties of exponentially harmonic maps” in Partial Differential Equations, Part 1, 2 (Warsaw, 1990), Banach Center Publ.
27, Part 1, Vol. 2, Polish Acad. Sci., Warsaw, 1992, 129–136.Google Scholar
[4]
Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Math.
86 (1964), 109–160.Google Scholar
[5]
Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order, reprint of the 1998 original, Classics Math., Springer, Berlin, 2001.Google Scholar
[6]
Hong, J. Q. and Yang, Y. H., Some results on exponentially harmonic maps(in Chinese), Chinese Ann. Math. Ser. A
14 (1993), 686–691.Google Scholar
[7]
Lieberman, G. M., On the regularity of the minimizer of a functional with exponential growth, Comment. Math. Univ. Carolin.
33 (1992), 45–49.Google Scholar
[8]
Naito, H., On a local Holder continuity for a minimizer of the exponential energy functional, Nagoya Math. J.
129 (1993), 97–113.Google Scholar
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