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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 EulerLagrange 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 

Pages (fromto)  411–425 
Journal  Advances in Calculus of Variations 
Volume  5 
Issue number  4 
DOIs  
Publication status  Published  2012 
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Projects
 1 Finished

THE VARIATIONAL APPROACH TO BIHARMONIC MAPS
Engineering and Physical Sciences Research Council
1/09/09 → 28/02/13
Project: Research council