# Intrinsically biharmonic maps into homogeneous spaces

Peter Hornung, Roger Moser

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

## 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 411–425 Advances in Calculus of Variations 5 4 https://doi.org/10.1515/ACV.2011.018 Published - 2012