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arXiv · 1204.5430

On the homotopy Dirichlet problem for p-harmonic maps

Stefano Pigola·Giona Veronelli
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Abstract

In this two papers we deal with the relative homotopy Dirichlet problem for p-harmonic maps from compact manifolds with boundary to manifolds of non-positive sectional curvature. Notably, we give a complete solution to the problem in case the target manifold is either compact and a new proof in case it is rotationally symmetric or two dimensional and simply connected. The proof of the compact case uses some ideas of White to define the relative d-homotopy type of Sobolev maps, and the regularity theory by Hardt and Lin. To deal with non-compact targets we introduce a periodization procedure which permits to reduce the problem to the previous one. Also, a general uniqueness result is given.

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Stefano Pigola, Giona Veronelli. 2015-02-05. On the homotopy Dirichlet problem for p-harmonic maps. https://arxiv.org/abs/1204.5430

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