Weak compactness of biharmonic maps

Abstract

This article shows that if a sequence of weak solutions of a perturbed biharmonic map satisfies $Phi_ko 0$ in $(W^{2,2})^*$ and $u_kightharpoonup u$ 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.

Keywords

• Biharmonic maps
• conservation law
• weak compactness