Harmonic maps from Riemannian polyhedra to geodesic spaces with curvature bounded from above
Harmonic maps from Riemannian polyhedra to geodesic spaces with curvature bounded from above
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DOI：
10.1007/s00526-007-0107-8
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发表时间：
2007-06
影响因子：
2.1
通讯作者：
B. Fuglede
中科院分区：
文献类型：
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作者：
B. Fuglede
在曲率≤ 1的测地空间中，去掉了关于从黎曼多面体（X，g）到半径R < π/2（最佳可能）的适当球B的局部能量极小映射的内部Hölder连续性的一个较早结果中关于目标局部紧性的假设.进一步证明了开集B上调和映射的变分Dirichlet问题是唯一可解的，且解在<$Ω的任意正则点上连续到边界<$Ω，在该正则点上给定的边界映射是连续的.
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 ballBof radiusR< π/2 (best possible) in a geodesic space with curvature ≤ 1. Furthermore, the variational Dirichlet problem for harmonic maps from an open settoBis 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.