Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 190, pp. 1-7.

Title: Weak compactness of biharmonic maps
 
Author: Shenzhou Zheng (Beijing Jiaotong Univ. Beijing, China)

Abstract:
 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.