## Analysis & PDE

### Energy identity for intrinsically biharmonic maps in four dimensions

#### Abstract

Let $u$ be a mapping from a bounded domain $S⊂ℝ4$ into a compact Riemannian manifold $N$. Its intrinsic biharmonic energy $E2(u)$ is given by the squared $L2$-norm of the intrinsic Hessian of $u$. We consider weakly converging sequences of critical points of $E2$. 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 $E2$.

#### Article information

Source
Anal. PDE, Volume 5, Number 1 (2012), 61-80.

Dates
Revised: 24 November 2010
Accepted: 25 January 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.apde/1513731197

Digital Object Identifier
doi:10.2140/apde.2012.5.61

Mathematical Reviews number (MathSciNet)
MR2957551

Zentralblatt MATH identifier
1273.58007

#### Citation

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

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