Radial Symmetry of p-Harmonic Minimizers
Abstract
“It is still not known if the radial cavitating minimizers obtained
by Ball [J.M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear
elasticity, Phil. Trans. R. Soc. Lond. A 306 (1982) 557–611] (and
subsequently by many others) are global minimizers of any physically reasonable
nonlinearly elastic energy”. The quotation is from [37] 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.
Main Authors
Format
Articles
Research article
Published
2018
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201810034327Use this for linking
Review status
Peer reviewed
ISSN
0003-9527
DOI
https://doi.org/10.1007/s00205-018-1246-0
Language
English
Published in
Archive for Rational Mechanics and Analysis
Citation
- Koski, A., & Onninen, J. (2018). Radial Symmetry of p-Harmonic Minimizers. Archive for Rational Mechanics and Analysis, 230(1), 321-342. https://doi.org/10.1007/s00205-018-1246-0
License
Copyright© Springer-Verlag GmbH Germany, part of Springer Nature 2018