Global solutions to the heat flow for $m$-harmonic maps and regularity Verena BoegeleinFrank DuzaarChristoph Scheven 58E2058J3535K5135B40$m$-harmonic mapsgradient flowglobal solutionsasymptotic behavior 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. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4819 10.1512/iumj.2012.61.4819 en Indiana Univ. Math. J. 61 (2012) 2157 - 2210 state-of-the-art mathematics http://iumj.org/access/