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arXiv 1004.22982010-04-14math.AP

双调和映射松弛能量极小元的部分正则性

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

Min-Chun Hong, Hao Yin

备注：: 25 pages

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摘要：

本文研究了从$m$维区域到球面的双调和映射的弛豫能。利用一种近似方法，证明了Hessian能量的松弛能量的极小元的存在性，并且证明了该极小元在有限$(m-4)$维Hausdorff测度的奇异集$Σ$外是双调和光滑的.此外，当$m=5$，我们证明了奇异集$Σ$是1-可求长的。

英文摘要：

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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