IUMJ

Title: Global solutions to the heat flow for $m$-harmonic maps and regularity

Authors: Verena Boegelein, Frank Duzaar and Christoph Scheven

Issue: Volume 61 (2012), Issue 6, 2157-2210

Abstract:

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 $\Omega$ with non-empty boundary $\partial\Omega$ into a compact Riemannian manifold $N$ without boundary subject to a Cauchy-Dirichlet condition posed on $\partial_{par}\Omega_{\infty}$. Moreover, in the case that $N$ has non-positive sectional curvature, we construct a solution with H\"older continuous spatial gradient.