Analysis & PDE

Energy identity for intrinsically biharmonic maps in four dimensions

Peter Hornung and Roger Moser

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Abstract

Let u be a mapping from a bounded domain S4 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
Received: 4 November 2009
Revised: 24 November 2010
Accepted: 25 January 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc. 35J35: Variational methods for higher-order elliptic equations

Keywords
biharmonic map energy identity bubbling

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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