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Analytic aspects of the harmonic map problem. (English) Zbl 0551.58011
Seminar on nonlinear partial differential equations, Publ., Math. Sci. Res. Inst. 2, 321-358 (1984).
[For the entire collection see Zbl 0542.00009.]
The author unifies and simplifies several analytic aspects of harmonic maps, especially those involving smoothness of weakly harmonic maps, as well as a priori estimates. He provides new simplified proofs of known results. And some new ones: (1) An estimate (a special case of joint work with K. Uhlenbeck) for maps with small energy - based on a monotonicity inequality of Schoen-Uhlenbeck and Price. (2) An improvement of a theorem of M. Grüter [J. Reine Angew. Math. 329, 1-15 (1981; Zbl 0461.53029)] to the effect that a weakly harmonic weakly comformal map of a surface is smooth. The author gives a pretty argument weakening the requirement of weak conformality.
Reviewer: J.Eells

MSC:
58E20 Harmonic maps, etc.