Partial Regularity of a minimizer of the relaxed energy for biharmonic maps

Min-Chun Hong; Hao Yin

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arXiv · 1004.2298

Partial Regularity of a minimizer of the relaxed energy for biharmonic maps

Min-Chun Hong·Hao Yin

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Abstract

In this paper, we study the relaxed energy for biharmonic maps from a $m$-dimensional domain into spheres. By an approximation method, we prove the existence of a minimizer of the relaxed energy of the Hessian energy, and that the minimizer is biharmonic and smooth outside a singular set $Σ$ of finite $(m-4)$-dimensional Hausdorff measure. Moreover, when $m=5$, we prove that the singular set $Σ$ is 1-rectifiable.

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Min-Chun Hong, Hao Yin. 2010-04-14. Partial Regularity of a minimizer of the relaxed energy for biharmonic maps. https://arxiv.org/abs/1004.2298

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