Radial Symmetry of p-Harmonic Minimizers
Koski, A., & Onninen, J. (2018). Radial Symmetry of p-Harmonic Minimizers. Archive for Rational Mechanics and Analysis, 230 (1), 321-342. doi:10.1007/s00205-018-1246-0
Published inArchive for Rational Mechanics and Analysis
© Springer-Verlag GmbH Germany, part of Springer Nature 2018
“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  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.