Harmonic maps from Riemannian polyhedra to geodesic spaces with curvature bounded from above

摘要

The hypothesis of local compactness of the target is removed from an earlier result about interior Hölder continuity of locally energy minimizing maps ϕ from a Riemannian polyhedron (X, g) to a suitable ball B of radius R < π/2 (best possible) in a geodesic space with curvature ≤ 1. Furthermore, the variational Dirichlet problem for harmonic maps from an open set $Omega Subset X$ to B is shown to be uniquely solvable, and the solution is continuous up to the boundary ∂Ω at any regular point of ∂Ω at which the prescribed boundary map is continuous.