In this paper we solve the relative homotopy Dirichlet problem for p-harmonic maps from compact manifolds with boundary to compact manifolds of non-positive sectional curvature. The proof, which is based on the direct calculus of variations, uses some ideas of B. White to define the relative d-homotopy type of Sobolev maps. One of the main points of the proof consists in showing that the regularity theory by Hardt and Lin can be applied. A comprehensive uniqueness result for general complete targets with non-positive curvature is also given.

On the Dirichlet problem for p-harmonic maps I: compact targets

PIGOLA, STEFANO;VERONELLI, GIONA
2015-01-01

Abstract

In this paper we solve the relative homotopy Dirichlet problem for p-harmonic maps from compact manifolds with boundary to compact manifolds of non-positive sectional curvature. The proof, which is based on the direct calculus of variations, uses some ideas of B. White to define the relative d-homotopy type of Sobolev maps. One of the main points of the proof consists in showing that the regularity theory by Hardt and Lin can be applied. A comprehensive uniqueness result for general complete targets with non-positive curvature is also given.
2015
Pigola, Stefano; Veronelli, Giona
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2049144
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