# Partial Regularity of Polyharmonic Maps to Targets of Sufficiently Simple Topology

### Andreas Gastel

Universität Duisburg-Essen, Germany

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## Abstract

We prove that polyharmonic maps $\mathbb R^m \supset \Omega \to N$ locally minimizing $\int|D^kf|^2\,dx$ 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

$\pi_1(N)=\ldots=\pi_{2k-1}(N)=0.$

## Cite this article

Andreas Gastel, Partial Regularity of Polyharmonic Maps to Targets of Sufficiently Simple Topology. Z. Anal. Anwend. 35 (2016), no. 4, pp. 397–410

DOI 10.4171/ZAA/1571