On the Dirichlet problem for \(p\)-harmonic maps. I: Compact targets (Q2516432)

The authors 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 uses some ideas of B. White to define the relative \(d\)-homotopy type of Sobolev maps, and the regularity theory by Hardt and Lin. A comprehensive uniqueness result for general complete targets with non-positive curvature is also given.