Electron. J. Diff. Equ., Vol. 2012 (2012), No. 190, pp. 1-7.

Weak compactness of biharmonic maps

Shenzhou Zheng

This article shows that if a sequence of weak solutions of a perturbed biharmonic map satisfies $\Phi_k\to 0$ in $(W^{2,2})^*$ and $u_k\rightharpoonup u$ weakly in $W^{2,2}$, then $u$ is a biharmonic map. In particular, we show that the space of biharmonic maps is sequentially compact under the weak- $W^{2,2}$ topology.

Submitted July 15,2012. Published October 31, 2012.
Math Subject Classifications: 35J48, 35G50, 58J05.
Key Words: Biharmonic maps, conservation law, weak compactness.

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Shenzhou Zheng
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: shzhzheng@bjtu.edu.cn, Tel: +1-859-257-4802

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