JournalszaaVol. 35, No. 4pp. 397–410

Partial Regularity of Polyharmonic Maps to Targets of Sufficiently Simple Topology

  • Andreas Gastel

    Universität Duisburg-Essen, Germany
Partial Regularity of Polyharmonic Maps to Targets of Sufficiently Simple Topology cover

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Abstract

We prove that polyharmonic maps RmΩN\mathbb R^m \supset \Omega \to N locally minimizing Dkf2dx\int|D^kf|^2\,dx are smooth on the interior of Ω\Omega outside a closed set Σ\Sigma with Hm2k(Σ)=0{\mathcal H}^{m-2k}(\Sigma)=0, provided that the target manifold NRnN \subset \mathbb R^n is smooth, closed, and fulfills

π1(N)==π2k1(N)=0.\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