Energy identity for intrinsically biharmonic maps in four dimensions

Peter Hornung, Roger Moser

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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 E1.
Original languageEnglish
Pages (from-to)61-80
Number of pages21
JournalAnalysis & PDE
Volume5
Issue number1
DOIs
Publication statusPublished - 2012

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