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### Abstract

The tension field $\tau(u)$ of a map $u$ from a domain $\Omega \subset \mathbb{R}^m$ into a manifold $N$ is the
negative $L^2$-gradient of the Dirichlet energy. In this paper we study critical points of the intrinsic biharmonic energy functional $T(u) = \int_\Omega |\tau(u)|^2$ when $N$ is a homogeneous space. We derive an Euler-Lagrange equation which makes sense for all critical points of $T$, in contrast to previously known versions. We also obtain a partial regularity result for solutions to this equation for arbitrary domain dimension.

Original language | English |
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Pages (from-to) | 411–425 |

Journal | Advances in Calculus of Variations |

Volume | 5 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2012 |

## Fingerprint Dive into the research topics of 'Intrinsically biharmonic maps into homogeneous spaces'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### THE VARIATIONAL APPROACH TO BIHARMONIC MAPS

Engineering and Physical Sciences Research Council

1/09/09 → 28/02/13

Project: Research council

## Cite this

Hornung, P., & Moser, R. (2012). Intrinsically biharmonic maps into homogeneous spaces.

*Advances in Calculus of Variations*,*5*(4), 411–425. https://doi.org/10.1515/ACV.2011.018