Regularity and relaxed problems of minimizing biharmonic maps into spheres期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Regularity and relaxed problems of minimizing biharmonic maps into spheres

Authors:	Min-Chun Hong Changyou Wang

Institution:	(1) Department of Mathematics, University of Queensland, QLD 4072 Brisbane, Australia;(2) Department of Mathematics, University of Kentucky, KY 40506 Lexington, USA

Abstract:	For $n\ge 5$ and $k\ge 4$ , we show that any minimizing biharmonic map from $\Omega\subset \Bbb R^n$ to S^k is smooth off a closed set whose Hausdorff dimension is at most n-5. When n = 5 and k = 4, for a parameter $\lambda\in 0,1]$ we introduce a $\lambda$ -relaxed energy $\Bbb H_{\lambda}$ of the Hessian energy for maps in $W^{2,2}(\Omega ; S^4)$ so that each minimizer $u_{\lambda}$ of $\Bbb H_{\lambda}$ is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of $\Bbb H_{\lambda}$ for $\lambda \in 0,1)$ .Received: 5 April 2004, Accepted: 19 October 2004, Published online: 10 December 2004

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