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A regularity result for polyharmonic maps with higher integrability

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Abstract

We prove a regularity result for critical points of the polyharmonic energy \({E(u)=\int_\Omega\vert\nabla^k u\vert^2dx}\) in \({W^{k,2p}(\Omega,{\mathcal N})}\) with \({k\in{\mathbb N}}\) and p > 1. Our proof is based on a Gagliardo–Nirenberg-type estimate and avoids the moving frame technique. In view of the monotonicity formulae for stationary harmonic and biharmonic maps, we infer partial regularity in theses cases.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Gilles Angelsberg

  2. Departement für Mathematik, ETH Zürich, CH-8092, Zürich, Switzerland

    David Pumberger

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  1. Gilles Angelsberg
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  2. David Pumberger
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Correspondence to David Pumberger.

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Angelsberg, G., Pumberger, D. A regularity result for polyharmonic maps with higher integrability. Ann Glob Anal Geom 35, 63–81 (2009). https://doi.org/10.1007/s10455-008-9122-z

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