Approximate solutions to the Dirichlet problem for harmonic maps between hyperbolic spaces

Duc, Duong Minh; Tuyen, Truong Trung

Approximate solutions to the Dirichlet problem for harmonic maps between hyperbolic spaces

Authors

Description

Our main result in this paper is the following: Given $H^m, H^n$ hyperbolic spaces of dimensional $m$ and $n$ corresponding, and given a Holder function $f=(s^1,...,f^{n-1}):\partial H^m\to \partial H^n$ between geometric boundaries of $H^m$ and $H^n$. Then for each $ε>0$ there exists a harmonic map $u:H^m\to H^n$ which is continuous up to the boundary (in the sense of Euclidean) and $u|_{\partial H^m}=(f^1,...,f^{n-1},ε)$.