Communications in Analysis and Geometry

Volume 17 (2009)

Number 2

Regularity of polyharmonic maps in the critical dimension

Pages: 185 – 226

DOI: http://dx.doi.org/10.4310/CAG.2009.v17.n2.a2

Authors

Andreas Gastel (Department Mathematik der Friedrich-Alexander-Universität, Erlangen, Germany)

Christoph Scheven (Department Mathematik der Friedrich-Alexander-Universität, Erlangen, Germany)

Abstract

We prove regularity of weakly $m$-polyharmonic maps (extrinsicor intrinsic) from domains in $\R^n$ of dimension $n=2m\ge4$ tocompact Riemannian manifolds, thus extending a previous resultby Wang for the case $m=2$. Moreover, we prove smoothness ofH\"older \hbox{continuous} weakly polyharmonic maps for domainsin $\R^n$ of dimension $n\ge 2m$.

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