2012/04/24 by Stefano Pigola, Pigola, Stefano, Giona Veronelli +1
Mathematics · #58E20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:58E20
paper · pdf · doi:10.48550/arxiv.1204.5430
26 pages. Corrected typos and references. Changed structure of the paper (but results unchanged)
arxiv created 2015/02/05 · arxiv updated 2015/02/06
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.