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Archive for Rational Mechanics and Analysis

, Volume 230, Issue 1, pp 321–342 | Cite as

Radial Symmetry of p-Harmonic Minimizers

  • Aleksis Koski
  • Jani Onninen
Article
  • 61 Downloads

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.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland
  2. 2.Department of MathematicsSyracuse UniversitySyracuseUSA

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