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

Fuglede, Bent
January 2008
Calculus of Variations & Partial Differential Equations;Jan2008, Vol. 31 Issue 1, p99
Academic Journal
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.


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