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

Details Energy identity of approximate biharmonic maps to Riemannian manifolds and its application Energy identity of approximate biharmonic maps to Riemannian manifolds and its application

2011-12-29

arxiv.org/abs/1112.6362v1

Mathematics

Analysis of PDEs

22 pages

Scientific paper

We consider in dimension four weakly convergent sequences of approximate biharmonic maps to a Riemannian manifold with bi-tension fields bounded in $L^p$ for $p>\frac43$. 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 $\mathbb R^4$. As a corollary, we obtain an energy identity for the heat flow of biharmonic maps at time infinity.

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