Energy identity for a class of approximate biharmonic maps into sphere in dimension four

Details Energy identity for a class of approximate biharmonic maps into sphere in dimension four Energy identity for a class of approximate biharmonic maps into sphere in dimension four

2011-10-29

arxiv.org/abs/1110.6536v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

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 $\mathbb R^4$.

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