Intrinsically biharmonic maps into homogeneous spaces

Reference:

Hornung, P. and Moser, R., 2012. Intrinsically biharmonic maps into homogeneous spaces. Advances in Calculus of Variations, 5 (4), 411–425.

Related documents:

Official URL:

http://dx.doi.org/10.1515/ACV.2011.018

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.

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