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.

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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.

Details

Item Type Articles
CreatorsHornung, P.and Moser, R.
DOI10.1515/ACV.2011.018
Related URLs
URLURL Type
http://www.scopus.com/inward/record.url?scp=84870287320&partnerID=8YFLogxKUNSPECIFIED
DepartmentsFaculty of Science > Mathematical Sciences
Publisher StatementHornungMoser.pdf: The final publication is available at www.degruyter.com
RefereedYes
StatusPublished
ID Code23763