Energy identity of approximate biharmonic maps to Riemannian manifolds and its application (Q444886)

In dimension four, the authors study weakly convergent sequences of bi-harmonic maps to a Riemannian manifold with bi-tension fields bounded in \(L^p\), \(p>4/3\). They prove an energy identity that accounts for the loss of Hessian energy by the sum of Hessian energies of a finite number of nontrivial bi-harmonic maps on \(\mathbb{R}^4\). As a consequence, they obtain an energy identity for the heat flow of bi-harmonic maps at time infinity.