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Rotationally symmetric harmonic maps from a ball into a warped product manifold. (English) Zbl 0578.58008
Two problems for the existence of rotationally symmetric harmonic maps from a Euclidean unit ball $B\subset R\sp n$ or $R\sp n$ into a warped product manifold $N\sb f=[0,r\sb 0]\times f\sp{S\sp{n-1}}$ are considered.
Reviewer: L.G.Vulkov

58E20Harmonic maps between infinite-dimensional spaces
30F15Harmonic functions on Riemann surfaces
Full Text: DOI EuDML
[1] Baldes,A.: Stability and uniqueness properties of the equator map from a ball into an ellipsoid. Math. Z.185, 505--516(1984) · Zbl 0531.58018 · doi:10.1007/BF01236259
[2] Bishop,R.L., O’Neill,B.: Manifolds of negative curvature. Trans. Amer. Math. Soc.145, 1--49(1969) · Zbl 0191.52002 · doi:10.1090/S0002-9947-1969-0251664-4
[3] Hartman,P.: Ordinary differential equations. New York (1964) · Zbl 0125.32102
[4] Hildebrandt,S., Kaul,H., Widmann,K.O.: An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math.138, 1--16(1977) · Zbl 0356.53015 · doi:10.1007/BF02392311
[5] Jäger,W., Kaul,H.: Rotationally symmetric harmonic maps from a ball into a sphere and the regularity problem for weak solutions of elliptic systems. J. Reine Angew. Math.343, 146--161(1983) · Zbl 0516.35032
[6] LaSalle,J.P.: Stability theory for ordinary differenti differential equations. J. differential equations4, 57--65(1968) · Zbl 0159.12002 · doi:10.1016/0022-0396(68)90048-X