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We prove the uniqueness of solutions to Dirichlet problem for p-harmonic maps with images in a small geodesic ball of the target manifold. As a consequence, we show that such maps have Hölder continuous derivatives. This gives an extension of a result by Hildebrandt et al. (Acta Math 138:1–16, 1977) concerning harmonic maps. 相似文献
2.
On the Heat Flow for Harmonic Maps with Potential 总被引:2,自引:0,他引:2
Let (M, g) and (N, h) be twoconnected Riemannian manifolds without boundary (M compact,N complete). Let G C
(N): ifu: M N is a smooth map, we consider the functional E
G
(u) = (1/2)
M
[|du|2– 2G(u)]dV
M
and we study its associated heat equation. Inthe compact case, we recover a version of the Eells–Sampson theorem,while for noncompact target manifold N, we establishsuitable hypotheses and ensure global existence and convergence atinfinity. In the second part of the paper, we study phenomena of blowingup solutions. 相似文献
3.
Paul Baird Ali Fardoun Rachid Regbaoui 《Calculus of Variations and Partial Differential Equations》2006,27(1):75-104
We formulate an appropriate gradient flow in order to study the evolution of the Q-curvature to a prescribed function on a 4-manifold. For a class of prescribed functions, we show convergence and describe the asymptotic behaviour at infinity. 相似文献
4.
Fardoun Ali Regbaoui Rachid 《Calculus of Variations and Partial Differential Equations》2003,17(1):1-16
We study developing singularities for surfaces of rotation with free boundaries and evolving under volume-preserving mean curvature flow. We show that singularities form a finite, discrete set along the axis of rotation. We prove a monotonicity formula and conclude that type I singularities are asymtotically cylindrical. 相似文献
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