Analysis & PDE
- Anal. PDE
- Volume 5, Number 1 (2012), 61-80.
Energy identity for intrinsically biharmonic maps in four dimensions
Let be a mapping from a bounded domain into a compact Riemannian manifold . Its intrinsic biharmonic energy is given by the squared -norm of the intrinsic Hessian of . We consider weakly converging sequences of critical points of . 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 .
Anal. PDE, Volume 5, Number 1 (2012), 61-80.
Received: 4 November 2009
Revised: 24 November 2010
Accepted: 25 January 2011
First available in Project Euclid: 20 December 2017
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Hornung, Peter; Moser, Roger. Energy identity for intrinsically biharmonic maps in four dimensions. Anal. PDE 5 (2012), no. 1, 61--80. doi:10.2140/apde.2012.5.61. https://projecteuclid.org/euclid.apde/1513731197