Journal
MATHEMATISCHE ZEITSCHRIFT
Volume 258, Issue 2, Pages 347-362Publisher
SPRINGER
DOI: 10.1007/s00209-007-0175-7
Keywords
uniqueness and Liouville theorems; p-harmonic maps; energy estimates
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We investigate p-harmonic maps, p >= 2, from a complete non-compact manifold into a non-positively curved target. First, we establish a uniqueness result for the p-harmonic representative in the homotopy class of a constant map. Next, we derive a Caccioppoli inequality for the energy density of a p-harmonic map and we prove a companion Liouville type theorem, provided the domain manifold supports a Sobolev-Poincare inequality. Finally, we obtain energy estimates for a p-harmonic map converging, with a certain speed, to a given point.
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