Vol. 5, No. 1, 2012

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Energy identity for intrinsically biharmonic maps in four dimensions

Peter Hornung and Roger Moser

Vol. 5 (2012), No. 1, 61–80
Abstract

Let $u$ be a mapping from a bounded domain $S\subset {ℝ}^{4}$ into a compact Riemannian manifold $N$. Its intrinsic biharmonic energy ${E}_{2}\left(u\right)$ is given by the squared ${L}^{2}$-norm of the intrinsic Hessian of $u$. We consider weakly converging sequences of critical points of ${E}_{2}$. Our main result is that the energy dissipation along such a sequence is fully due to energy concentration on a finite set and that the dissipated energy equals a sum over the energies of finitely many entire critical points of ${E}_{2}$.

Keywords
biharmonic map, energy identity, bubbling
Mathematical Subject Classification 2000
Primary: 58E20, 35J35