  "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 [J. Sivaloganathan and S. J. Spector,
Necessary conditions for a minimum at a radial cavitating singularity in
nonlinear elasticity, Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008), no.
1, 201--213] 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.
