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–Poincaré inequality. Finally, we obtain energy estimates for a p-harmonic map converging, with a certain speed, to a given point.

Pigola, S., M., R., Setti, A. (2008). Constancy of p-harmonic maps of finite q -energy into non-positively curved manifolds. MATHEMATISCHE ZEITSCHRIFT, 258(2), 347-362 [10.1007/s00209-007-0175-7].

Constancy of p-harmonic maps of finite q -energy into non-positively curved manifolds

PIGOLA, STEFANO
;
2008

Abstract

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–Poincaré inequality. Finally, we obtain energy estimates for a p-harmonic map converging, with a certain speed, to a given point.
Articolo in rivista - Articolo scientifico
Uniqueness and Liouville theorems - p-Harmonic maps - Energy estimates
English
2008
258(2)
347
362
reserved
Pigola, S., M., R., Setti, A. (2008). Constancy of p-harmonic maps of finite q -energy into non-positively curved manifolds. MATHEMATISCHE ZEITSCHRIFT, 258(2), 347-362 [10.1007/s00209-007-0175-7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/271368
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