  We consdier in dimension four weakly convergent sequences of approximate
biharmonic maos into sphere with bi-tension fields bounded in $L^p$ for some
$p>1$. We prove an energy identity that accounts for the loss of Hessian
energies by the sum of Hessian energies over finitely many nontrivial
biharmonic maps on $\mathbb R^4$.

Analysis of PDEs;Differential Geometry