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Annals of Global Analysis and Geometry

, Volume 35, Issue 1, pp 63–81 | Cite as

A regularity result for polyharmonic maps with higher integrability

  • Gilles Angelsberg
  • David PumbergerEmail author
Original Paper

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.

Keywords

Polyharmonic maps Harmonic maps Biharmonic maps Gagliardo–Nirenberg inequality 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Departement für MathematikETH ZürichZürichSwitzerland

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