Radial Symmetry of p-Harmonic Minimizers

Aleksis Koski, Jani Onninen

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

“It is still not known if the radial cavitating minimizers obtained by Ball (Philos Trans R Soc Lond A 306:557–611, 1982) (and subsequently by many others) are global minimizers of any physically reasonable nonlinearly elastic energy”. This quotation is from Sivaloganathan and Spector (Ann Inst Henri Poincaré Anal Non Linéaire 25(1):201–213, 2008) and seems to be still accurate. The model case of the p-harmonic energy is considered here. We prove that the planar radial minimizers are indeed the global minimizers provided we prescribe the admissible deformations on the boundary. In the traction free setting, however, even the identity map need not be a global minimizer.

Original languageEnglish (US)
Pages (from-to)321-342
Number of pages22
JournalArchive for Rational Mechanics and Analysis
Volume230
Issue number1
DOIs
StatePublished - Oct 1 2018

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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