Energy identity for a class of approximate biharmonic maps into sphere   in dimension four
  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 $\mathbb R^4$. 
Changyou Wang and Shenzhou Zheng
math.AP math.DG