6533b826fe1ef96bd12850c5
RESEARCH PRODUCT
Radial symmetry of p-harmonic minimizers
Jani OnninenJani OnninenAleksis Koskisubject
radial symmetryosittaisdifferentiaaliyhtälötMathematics - Complex VariablesMechanical Engineering010102 general mathematicsMathematical analysisSymmetry in biologyElastic energyp-harmonic minimizers01 natural sciencesfunktioteoria010101 applied mathematicssymbols.namesakeMathematics (miscellaneous)Poincaré conjecture35J60 30C70symbolsFOS: MathematicsIdentity functionBall (mathematics)0101 mathematicsComplex Variables (math.CV)AnalysisNon lineaireMathematicsdescription
"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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-10-03 |