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On a local Hölder continuity for a minimizer of the exponential energy functional

Published online by Cambridge University Press:  22 January 2016

Hisashi Naito
Hisashi Naito*
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Nagoya 464-01, Japan
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Let Ω ⊂ Rm be a bounded domain with smooth boundary, where m ≥ 2. We consider the exponential energy functional

for u: Ω→ Rn, where n ≥ 2.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 129 , March 1993 , pp. 97 - 113
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

[1] DiBenedetto, E., C1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Analysis: TMA, 7 (1983), 827–850.Google Scholar
[2] Due, D. M. and Eells, J., Regularity of exponentially harmonic function, to appear in Internat. J. Math.,Google Scholar
[3] Eells, J. and Lemaire, L., Some properties of exponential harmonic maps, preprint.Google Scholar
[4] Giaquinta, M., “Multiple Integrals in the Calculus of Variations and Nonlinear Analysis,” Princeton Univ. Press, Princeton, New Jersey, 1983.Google Scholar
[5] Giaquinta, M. and Giusti, E., On the regularity of the minima of variational integrals, Acta Math., 148 (1982), 31–46.Google Scholar
[6] Gilberg, D. and Trudinger, N. S., “Elliptic Partial Differential Equations of Second Order, Second edition,” Springer-Verlag, Berlin-Heiderberg-New York, 1983.Google Scholar
[7] Hardt, R. and Lin, F. H., Mapping minimizing the Lp -norm of the gradient, Comm. Pure and Appl. Math., 40 (1987), 555–588.Google Scholar
[8] Masuda, K., “Nonlinear Mathematics,” Asakura, Tokyo, 1985. (in Japanese)Google Scholar
[9] Morrey, C. B., “Multiple Integrals in the Calculus of Variations,” Springer-Verlag, Berlin-Heiderberg-New York, 1966.CrossRefGoogle Scholar
[10] Schoen, R. and Uhlenbeck, K., A regularity theory for harmonic maps, J. Differential Geom., 18 (1982), 307–335.Google Scholar
[11] Tolksdorff, P., Everywhere regularity for some quasi-linear system with a lack of ellipticity, Annali di Math. Pure et Applicata, 134 (1983), 241–266.Google Scholar
[12] Uhlenbeck, K., Regularity of nonlinear elliptic systems, Acta Math., 138 (1977), 219–240.CrossRefGoogle Scholar
[13] White, B., Homotopy classes in Sobolev spaces and the existence of energy minimizing maps, Acta Math., 160 (1988), 1–17.CrossRefGoogle Scholar