Partial Regularity of Polyharmonic Maps to Targets of Sufficiently Simple Topology

Abstract

We prove that polyharmonic maps ${\mathbb{R}}^m\supset \Omega \to N$ locally minimizing $\int |D^{k}f{|}^{2}dx$ are smooth on the interior of $\Omega$ outside a closed set $\Sigma$ with ${\mathcal{H}}^{m-2k}(\Sigma )=0$, provided that the target manifold $N\subset {\mathbb{R}}^n$ is smooth, closed, and fulfills