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A regularity result for polyharmonic maps with higher integrability

Angelsberg, Gilles ; Pumberger, David

In: Annals of Global Analysis and Geometry, 2009, vol. 35, no. 1, p. 63-81

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    Title
    • A regularity result for polyharmonic maps with higher integrability
    Author
    • Angelsberg, Gilles. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA
    • Pumberger, David. Departement für Mathematik, ETH Zürich, CH-8092, Zürich, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Annals of Global Analysis and Geometry, 2009, vol. 35, no. 1, p. 63-81. Springer Netherlands
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:319615
    Summary
    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