Global Solutions to the Heat Flow for m-harmonic Maps and Regularity

摘要

In this paper, we establish the existence of global weak solutions to the heat flow for m-harmonic maps from a compact m-dimensional Riemannian manifold Ω with non-empty boundary ?Ω into a compact Riemannian manifold N without boundary subject to a Cauchy-Dirichlet condition posed on ?_(par)Ω_∞. Moreover, in the case that N has non-positive sectional curvature, we construct a solution with H?lder-continuous spatial gradient.